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Jean Van Schaftingen

Curriculum vitæ

Expérience professionnelle

à partir d’octobre 2021
Professeur ordinaire, Université catholique de Louvain, Faculté des Sciences (SC) et Institut de Recherche en Mathématique et Physique (IRMP), Louvain-la-Neuve, Belgique
octobre 2015–septembre 2021
Professeur, Université catholique de Louvain, Faculté des Sciences (SC) et Institut de Recherche en Mathématique et Physique (IRMP), Louvain-la-Neuve, Belgique.
octobre 2007–septembre 2015
Chargé de cours, à titre définitif depuis octobre 2010, Université catholique de Louvain, Faculté des Sciences (SC) et Institut de Recherche en Mathématique et Physique (IRMP), Louvain-la-Neuve, Belgique.
octobre 2006–septembre 2007
Chargé de recherches du Fonds National de la Recherche Scientifique, Université catholique de Louvain (UCLouvain), Département de Mathématique, Unité d’analyse mathématique et de mécaniqueLouvain-la-Neuve, Belgique.
octobre 2002–septembre 2006
Aspirant du Fonds National de la Recherche Scientifique, Université catholique de Louvain, Département de Mathématique, Unité d’analyse mathématique et de mécanique, Louvain-la-Neuve, Belgique.

Formation académique

19 mai 2005
Docteur en sciences mathématiques, Université catholique de Louvain.
Titre de la dissertation : Symmetrizations, Symmetry of Critical Points and \(L^1\) Estimates.
Membres du jury : Michel Willem (promoteur, UCLouvain), Jean Mawhin (président), Thomas Bartsch (Universität Giessen), Haïm Brezis (Université de Paris VI), Thierry De Pauw (UCLouvain), Jean-Pierre Gossez (Université Libre de Bruxelles) et Patrick Habets (UCLouvain).
juin 2003
Diplôme d’études approfondies interuniversitaire en mathématiques, Université catholique de Louvain.
Travail de DEA : Symétrisations: mesure, géométrie et approximation, promoteur : Michel Willem.
juin 2002
Ingénieur civil en mathématiques appliquées, Université catholique de Louvain, la plus grande distinction avec les félicitations du jury. Travail de fin d’études : Symétrisations et problèmes elliptiques non linéaires, promoteur : Michel Willem.

Expérience pédagogique

2001–2002
Étudiant–moniteur, Mécanique des milieux continus, Faculté des Sciences appliquées
2002–2005
Encadrement des exercices d’Analyse fonctionnelle pour les étudiants de licence en mathématiques et de Compléments d’analyse pour les étudiants ingénieurs civils en mathématiques appliquées.

Prix scientifiques

2006
Concours annuel de la Classe des Sciences de l’Académie royale des Sciences, des Lettres et des Beaux-Arts de Belgique, Groupe I – Mathématiques pour une “contribution originale à l’étude du rôle de la symétrie dans les problèmes non linéaires”.
2011
Prix Adolphe Wetrems, sciences mathématiques et physiques.
2020
Prix Jacques Deruyts, récompensant l’auteur de travaux originaux dans le domaine de l’analyse mathématique, Académie royale des Sciences, des Lettres et des Beaux-Arts de Belgique.

Financements

2009–2012
Crédit aux chercheurs FC 64984 - 1.5.058.09.F F.R.S.-FNRS, «Propriétes d’espaces de Sobolev et équations aux dérivées partielles elliptiques semilinéaires»
2010–2014
Projet 2.4.550.10.F du Fonds de la Recherche Fondamentale Collective, «Étude qualitative des solutions d’équations aux dérivées partielles elliptiques variationnelles. Symétries, bifurcations, singularités, multiplicité et méthodes numériques.» Promoteurs : D. Bonheure (ULB, promoteur principal), C. Troestler (UMons) et J. Van Schaftingen (UCLouvain).
2013–2014
Crédit aux chercheurs J.044.13.F F.R.S.-FNRS «Problèmes vectoriels en EDP : Équation de Choquard et inégalités pour des champs de vecteurs».
2014–2018
Projet T.1110.14 du Fonds de la Recherche Fondamentale Collective intitulé «Existence et popriétés asymptotiques de solutions de systèmes d’équations aux dérivées partielles elliptiques semilinéaires», promoteurs: D. Bonheure (ULB), C. Troestler (UMons, promoteur principal) et J. Van Schaftingen (UCLouvain).
2017–2018
Mandat d’Impulsion Scientifique (MIS) F.452317 du Fonds de la Recherche Scientifique–FNRS «Topological singularities of Sobolev maps between manifolds for the weak-bounded approximation and lifting problems».
2021–2024
Projet de Recherche (PDR) T.0229.21 du Fonds de la Recherche Scientifique–FNRS SHarMAGLaR «Applications harmoniques singulières et asymptotique de relaxations de Ginzburg–Landau».

Séjours scientifiques

18 janvier 2004–12 mars 2004
Laboratoire J.-L. Lions, Université de Paris 6, France.
1ᵉʳ–9 décembre 2004
Rutgers University, New Brunswick, New Jersey, États-Unis d’Amérique.
14–28 février 2005
Courant Institute for the Mathematical Sciences, New York University, États-Unis d’Amérique.
avril 2005
Laboratoire J.-L. Lions, Université de Paris 6.
novembre 2005–juin 2006
Laboratoire J.-L. Lions, Université de Paris 6.
27 novembre 2006–5 décembre 2006
Rutgers University, New Brunswick, New Jersey, États-Unis d’Amérique.
8–17 janvier 2008
Rutgers University, New Brunswick, New Jersey, États-Unis d’Amérique.
2–12 février 2009
Rutgers University, New Brunswick, New Jersey, États-Unis d’Amérique.
18–27 janvier 2011
Rutgers University, New Brunswick, New Jersey, États-Unis d’Amérique.
14 janvier–20 mars 2019
University of Oxford, Mathematical Institute, Royaume-Uni, Academic visitor.

Publications

Soumises
, The extension of traces for Sobolev mappings between manifolds.
, et , Limiting behavior of minimizing \(p\)–harmonic maps in 3d as \(p\) goes to \(2\) with finite fundamental group.
et , Singular extension of critical Sobolev mappings under an exponential weak-type estimate.
, Injective ellipticity, cancelling operators, and endpoint Gagliardo-Nirenberg-Sobolev inequalities for vector fields.
Acceptées
, Lifting of fractional Sobolev mappings to noncompact covering spaces, à paraître dans Ann. Inst. H. Poincaré Anal. Non Linéaire
2024
, , et , Families of functionals representing Sobolev norms, Anal. PDE 17 (2024), n°3, 943–979.
, Endpoint Sobolev inequalities for vector fields and cancelling operators, in Duván Cardona, Joel Restrepo et Michael Ruzhansky (eds.), Extended Abstracts 2021/2022. Methusalem Lectures, Birkhäuser, Cham, Trends in Mathematics, No. 3, 2024, 47–56.
, et , Boundary ellipticity and limiting \(L^1\)-estimates on halfspaces, Adv. Math. 439 (2024), 109490 (25 pages).
2023
et , Asymptotic behavior of minimizing \(p\)-harmonic maps when \(p \nearrow 2\) in dimension \(2\), Calc. Var. Partial Differential Equations 62 (2023), 229 (45 pages).
, Fractional Gagliardo-Nirenberg interpolation inequality and bounded mean oscillation, C. R. Math. Acad. Sci. Paris 361 (2023), 1041–1049.
, Limiting Sobolev estimates for vector fields and cancelling differential operators, in Jaroslav Lukeš, Zdeněk Mihula, Luboš Pick et Hana Turčinová (eds.), Function spaces and applications XII (Pazeky nad Jizerou, 2023), MatfyzPress, Charles University, Prague, 2023, 135–152.
et , Quantitative characterization of traces of Sobolev maps, Commun. Contemp. Math. 25 (2023), n°02, 2250003 (31 pages).
, , , et , Spaces of Besov–Sobolev type and a problem on nonlinear approximation, J. Funct. Anal. 284 (2023), n°4, 109775.
2022
, , et , Sobolev spaces revisited, Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 33 (2022), n°2, 413–437.
et , Limiting Sobolev and Hardy inequalities on stratified homogeneous groups, Annal. Acad. Sc. Fennic. 47 (2022), n°2, 1065–1098.
, et , Renormalised energies and renormalisable singular harmonic maps into a compact manifold on planar domains, Math. Annal. 383 (2022), 1061–1125.
, Reverse superposition estimates in Sobolev spaces, Pure Appl. Funct. Anal. 7 (2022), n°2, 805–811.
2021
, et , On limiting trace inequalities for vectorial differential operators, Indiana Univ. Math. J. 70 (2021), n°5, 2133–2176.
, et , Ginzburg-Landau relaxation for harmonic maps on planar domains into a general compact vacuum manifold, Arch. Rat. Mech. Anal. 242 (2021), n°2, 875–935.
et , Lifting in compact covering spaces for fractional Sobolev mappings, Anal. PDE 14 (2021), n°6, 1851–1871.
et , Trace theory for Sobolev mappings into a manifold, Ann. Fac. Sci. Toulouse Math. (6) 30 (2021), n°2, 281–299.
, et , Going to Lorentz when fractional Sobolev, Gagliardo and Nirenberg estimates fail, Calc. Var. Partial Differential Equations 60 (2021), n°129
, et , A surprising formula for Sobolev norms, Proc. Natl. Acad. Sci. USA 118 (2021), n°8, e2025254118.
et , Metric characterization of the sum of fractional Sobolev spaces, Stud. Math. 258 (2021), 27–51.
2020
et , Estimates of the amplitude of holonomies by the curvature of a connection on a bundle, Pure Appl. Funct. Anal. 5 (2020), n°4, 891–897.
et , Characterization of the traces on the boundary of functions in magnetic Sobolev spaces, Adv. Math. 371 (2020), 107246.
, et , Groundstates for Choquard type equations with Hardy–Littlewood–Sobolev lower critical exponent, Proc. Roy. Soc. Edinb. A 150 (2020), n°3, 1377–1400.
et , Range convergence monotonicity for vector measures and range monotonicity of the mass, Ric. Mat. 69 (2020), n°1, 293-326.
et , An estimate of the Hopf degree of fractional Sobolev mappings, Proc. Amer. Math. Soc. 148 (2020), n°7, 2877–2891.
et , Vortex motion for the lake equations, Comm. Math. Phys. 375 (2020), n°2, 1459–1501.
2019
, Estimates by gap potentials of free homotopy decompositions of critical Sobolev maps, Adv. Nonlinear Anal. 9 (2019), n°1, 1214–1250.
et , Optimal embeddings into Lorentz spaces for some vector differential operators via Gagliardo’s lemma, Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 30 (2019), n°3, 413–436.
, , et , Representing three-dimensional cross fields using fourth order tensors, in Roca X. et Loseille A. (eds.), 27th International Meshing Roundtable. IMR 2018, Springer, Cham, Lecture Notes in Computational Science and Engineering, No. 127, 2019, 89–108.
et , Higher order intrinsic weak differentiability and Sobolev spaces between manifolds, Adv. Calc. Var. 12 (2019), n°3, 303–332.
, et , Properties of groundstates of nonlinear Schrödinger equations under a weak constant magnetic field, J. Math. Pures Appl. (9) 124 (2019), 123–168.
et , Uniform boundedness principles for Sobolev maps into manifolds, Ann. Inst. H. Poincaré Anal. Non Linéaire 36 (2019), n°2, 417–449.
2018
, , , et , Sharp Gagliardo-Nirenberg inequalities in fractional Coulomb–Sobolev spaces, Trans. Amer. Math. Soc. 370 (2018), n°11, 8285–8310.
et , Groundstates of the Choquard equations with a sign-changing self-interaction potential, Z. Angew. Math. Phys. 69 (2018), n°3, 69:86.
et , Groundstates for a local nonlinear perturbation of the Choquard equations with lower critical exponent, J. Math. Anal. Appl. 464 (2018), n°2, 1184–1202.
, et , Weak approximation by bounded Sobolev maps with values into complete manifolds, C. R. Math. Acad. Sci. Paris 356 (2018), n°3, 264–271.
, Sobolev mappings: from liquid crystals to irrigation via degree theory, Lecture notes of the Godeaux Lecture delivered at the 9th Brussels Summer School of Mathematics (2018)
et , Odd symmetry of least energy nodal solutions for the Choquard equation, J. Differential Equations 264 (2018), n°2, 1231–1262.
2017
et , Gauge-measurable functions, Rend. Istit. Mat. Univ. Trieste 49 (2017), 113–135.
, , et , Semiclassical Sobolev constants for the electro-magnetic Robin Laplacian, J. Math. Soc. Japan 69 (2017), n°4, 1667–1714.
, et , Density of bounded maps in Sobolev spaces into complete manifolds, Ann. Mat. Pura Appl. (4) 196 (2017), n°6, 2261–2301.
et , Approximation of symmetrizations by Markov processes, Indiana Univ. Math. J. 66 (2017), n°4, 1145–1172.
et , Standing waves with a critical frequency for nonlinear Choquard equations, Nonlinear Anal. 161 (2017), 87–107.
, et , The logarithmic Choquard equation: sharp asymptotics and nondegeneracy of the groundstate, J. Funct. Anal. 272 (2017), n°12, 5255–5281.
, et , Bourgain–Brezis estimates on symmetric spaces of non-compact type, J. Funct. Anal. 273 (2017), n°4, 1504-1547.
et , Existence of groundstates for a class of nonlinear Choquard equations in the plane, Adv. Nonlinear Stud. 17 (2017), n°3, 581–594.
, et , The incompressible Navier Stokes flow in two dimensions with prescribed vorticity, in Sagun Chanillo, Bruno Franchi, Guozhen Lu, Carlos Perez et Eric T. Sawyer (eds.), Harmonic Analysis, Partial Differential Equations and Applications, Birkhäuser, Applied and Numerical Harmonic Analysis, 2017, 19–25.
et , Controlled singular extension of critical trace Sobolev maps from spheres to compact manifolds, Int. Math. Res. Not. IMRN 2017 (2017), n°12, 3467–3683.
et , A guide to the Choquard equation, J. Fixed Point Theory Appl. 19 (2017), n°1, 773–813.
, et , An \(L^1\)–type estimate for Riesz potentials, Rev. Mat. Iberoam. 33 (2017), n°1, 291–304.
, et , Variations on a proof of a borderline Bourgain–Brezis Sobolev embedding theorem, Chinese Ann. Math. Ser. B 38 (2017), n°1, 235–252.
et , Choquard equations under confining external potentials, NoDEA Nonlinear Differential Equations Appl. 24 (2017), n°1, 1–24.
, et , Least action nodal solutions for the quadratic Choquard equation, Proc. Amer. Math. Soc. 145 (2017), n°2, 737–747.
2016
, et , Groundstates and radial solutions to nonlinear Schrödinger–Poisson–Slater equations at the critical frequency, Calc. Var. Partial Differential Equations 55 (2016), n°146, 58.
et , Nodal solutions for the Choquard equation, J. Funct. Anal. 271 (2016), n°1, 107–135.
et , Intrinsic colocal weak derivatives and Sobolev spaces between manifolds, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 16 (2016), n°1, 97–128.
, et , Applications of Bourgain–Brezis inequalities to fluid mechanics and magnetism, C. R. Math. Acad. Sci. Paris 354 (2016), n°1, 51–55.
et , Geometric partial differentiability on manifolds: the tangential derivative and the chain rule, J. Math. Anal. Appl. 435 (2016), n°2, 1672–1681.
2015
et , Groundstates of nonlinear Choquard equations: Hardy–Littlewood–Sobolev critical exponent, Commun. Contemp. Math. 17 (2015), n°5, 1550005 (12 pages).
et , Existence of groundstates for a class of nonlinear Choquard equations, Trans. Amer. Math. Soc. 367 (2015), n°9, 6557–6579.
et , Semiclassical stationary states for nonlinear Schrödinger equations under a strong external magnetic field, J. Differential Equations 259 (2015), n°2, 596–627.
, et , Strong density for higher order Sobolev spaces into compact manifolds, J. Eur. Math. Soc. (JEMS) 17 (2015), n°4, 763–817.
et , Semi-classical states for the Choquard equations, Calc. Var. Partial Differential Equations 52 (2015), n°1, 199–235.
et , Existence, stability and oscillation properties of slow decay positive solutions of supercritical elliptic equations with Hardy potential, Proc. Roy. Soc. Edinburgh Sect. A 58 (2015), n°1, 255–271.
2014
, Limiting Bourgain–Brezis estimates for systems of linear differential equations: Theme and variations, J. Fixed Point Theory Appl. 15 (2014), n°2, 273–297.
, et , Strong approximation of fractional Sobolev maps, J. Fixed Point Theory Appl. 15 (2014), n°1, 133–153.
et , Hardy–Sobolev inequalities for vector fields and canceling linear differential operators, Indiana Univ. Math. J. 63 (2014), n°5, 1419–1445.
, Equivalence between Pólya–Szegő and relative capacity inequalities under rearrangement, Arch. Math. (Basel) 103 (2014), n°4, 367–379.
, Interpolation inequalities between Sobolev and Morrey–Campanato spaces: A common gateway to concentration-compactness and Gagliardo–Nirenberg, Port. Math. 71 (2014), n°3–4, 159–175.
, Approximation in Sobolev spaces by piecewise affine interpolation, J. Math. Anal. Appl. 420 (2014), n°1, 40–47.
2013
, et , Density of smooth maps for fractional Sobolev spaces \(W^{s, p}\) into \(\ell\)–simply connected manifolds when \(s \ge 1\), Confluentes Math. 5 (2013), n°2, 3–22.
et , Desingularization of vortex rings and shallow water vortices by a semilinear elliptic problem, Arch. Rat. Mech. Anal. 210 (2013), n°2, 409–450.
, A direct proof of the existence of eigenvalues and eigenvectors by Weierstrass’s theorem, Amer. Math. Monthly 120 (2013), n°8, 741–746.
et , Groundstates of nonlinear Choquard equations: existence, qualitative properties and decay asymptotics, J. Funct. Anal. 265 (2013), n°2, 153–184.
et , Stationary solutions of the nonlinear Schrödinger equation with fast-decay potentials concentrating around local maxima, Calc. Var. Partial Differential Equations 47 (2013), n°1–2, 243–271.
, Limiting Sobolev inequalities for vector fields and canceling linear differential operators, J. Eur. Math. Soc. (JEMS) 15 (2013), n°3, 877–921.
et , Nonexistence and optimal decay of supersolutions to Choquard equations in exterior domains, J. Differential Equations 254 (2013), n°8, 3089–3145.
2012
et , Nonlocal Hardy type inequalities with optimal constants and remainder terms, Ann. Univ. Buchar. Math. Ser. 3 (LXI) (2012), n°2, 187–200.
et , Finding critical points whose polarization is also a critical point, Topol. Methods Nonlinear Anal. 40 (2012), n°2, 371–379.
, et , Nonlinear Schrödinger equation with unbounded or vanishing potentials: solutions concentrating on lower dimensional spheres, J. Differential Equations 252 (2012), n°1, 941–968.
2011
et , Extremal functions in Poincaré–Sobolev inequalities for functions of bounded variation, in Denis Bonheure, Mabel Cuesta, Enrique J. and Peter Takáč Lami Dozo, Jean Van Schaftingen et Michel Willem (eds.), Nonlinear Elliptic Partial Differential Equations, Amer. Math. Soc., Contemporary Mathematics, No. 540, 2011, 47–58.
2010
et , Desingularization of vortices for the Euler equation, Arch. Rat. Mech. Anal. 198 (2010), n°3, 869–925.
et , Groundstates for the nonlinear Schrödinger equation with potential vanishing at infinity, Ann. Mat. Pura Appl. (4) 189 (2010), 273–301.
et , Semiclassical stationary states for nonlinear Schrödinger equations with fast decaying potentials, Calc. Var. Partial Differential Equations 37 (2010), n°1, 1—27.
, Limiting fractional and Lorentz spaces estimates of differential forms, Proc. Amer. Math. Soc. 138 (2010), n°1, 235–240.
2009
et , Closure of Smooth Maps in \(W^{1,p}(B^3;S^2)\), Differential Integral Equations 22 (2009), n°9–10, 881–900.
, Explicit approximation of the symmetric rearrangement by polarizations, Arch. Math. (Basel) 93 (2009), n°2, 181–190.
et , Existence and concentration for nonlinear Schrödinger equations with fast decaying potentials, C. R. Math. Acad. Sci. Paris 347 (2009), n°15–16, 921–926.
, et , Pathological solutions to elliptic problems in divergence form with continuous coefficients, C. R. Math. Acad. Sci. Paris 347 (2009), n°13–14, 773–778.
et , Subelliptic Bourgain–Brezis estimates on groups, Math. Res. Lett. 16 (2009), n°3, 487–501.
2008
et , Circulation integrals and critical Sobolev spaces: problems of optimal constants, in Dorina Mitrea et Marius Mitrea (eds.), Perspectives in Partial Differential Equations, Harmonic Analysis and Applications, Amer. Math. Soc., Proc. Sympos. Pure Math., No. 79, 2008, 33–47.
, et , Periodic homogenization for convex functionals using Mosco convergence, Ricerche Mat. 57 (2008), n°2, 209–249.
, Estimates for \(\mathrm{L}^1\) vector fields under higher-order differential conditions, J. Eur. Math. Soc. (JEMS) 10 (2008), n°4, 867–882.
, , et , Asymptotics and symmetries of least energy nodal solutions of Lane–Emden problems with slow growth, Commun. Contemp. Math. 10 (2008), n°4, 609–631.
, et , A case of density in \(W^{2,p}(M;N)\), C. R. Math. Acad. Sci. Paris 346 (2008), n°13–14, 735–740.
et , Bound state solutions for a class of nonlinear Schrödinger equations, Rev. Mat. Iberoam. 24 (2008), n°1, 297–351.
et , Symmetry of solutions of semilinear elliptic problems, J. Eur. Math. Soc. (JEMS) 10 (2008), n°2, 439–456.
2007
, et , Periodic homogenization of monotone multivalued operators, Nonlinear Anal. 67 (2007), n°12, 3217–3239.
et , Boundary estimates for elliptic systems with \(L^1\)–data, Calc. Var. Partial Differential Equations 30 (2007), n°3, 369–388.
et , The continuity of functions with \(N\)–th derivative measure, Houston J. Math. 33 (2007), n°3, 927–939.
2006
, Approximation of symmetrizations and symmetry of critical points, Topol. Methods Nonlinear Anal. 28 (2006), n°1, 61–85.
, Anisotropic symmetrization, Ann. Inst. H. Poincaré Anal. Non Linéaire 23 (2006), n°4, 539–565.
, Function spaces between BMO and critical Sobolev spaces, J. Funct. Anal. 236 (2006), n°2, 490–516.
et , Nonlinear Schrödinger equations with potentials vanishing at infinity, C. R. Math. Acad. Sci. Paris 342 (2006), n°12, 903–908.
, Universal approximation of symmetrizations by polarizations, Proc. Amer. Math. Soc. 134 (2006), n°1, 177–186.
2005
et , Periodic reiterated homogenization for elliptic functions, J. Math. Pures Appl. (9) 84 (2005), n°12, 1716–1743.
, Symmetrization and minimax principles, Commun. Contemp. Math. 7 (2005), n°4, 463–481.
et , Reiterated homogenization for elliptic operators, C. R. Math. Acad. Sci. Paris 340 (2005), n°3, 209–214.
2004
, Estimates for \(L^1\) vector fields with a second order condition, Acad. Roy. Belg. Bull. Cl. Sci. (6) 15 (2004), n°1–6, 103–112.
et , Set transformations, symmetrizations and isoperimetric inequalities, in V. Benci et A. Masiello (eds.), Nonlinear analysis and applications to physical sciences, Springer Italia, Milan, 2004, 135–152.
, Estimates for \(L^1\)–vector fields, C. R. Math. Acad. Sci. Paris 339 (2004), n°3, 181–186.
, A simple proof of an inequality of Bourgain, Brezis and Mironescu, C. R. Math. Acad. Sci. Paris 338 (2004), n°1, 23–26.

Exposés sur invitation

25 février 2004
Groupe de travail – analyse non linéaire, Laboratoire J.-L. Lions, Université de Paris 6, Symétries de points critiques obtenus par des méthodes de minimax.
11 mars 2004
Groupe de travail – équations elliptiques et paraboliques non linéaires, Université de Paris 11, Symétrisations et symétries de solutions de problèmes variationnels.
2 décembre 2004
Joint Princeton, Institute for Advanced Study and Rutgers analysis seminar, Princeton University, \(L^1\) estimates for vector fields.
7 décembre 2004
Rutgers analysis seminar, Rutgers University, New Brunswick, New Jersey, États-Unis d’Amérique, Approximation of symmetrizations, random symmetrizations and symmetry of critical points.
17 février 2005
Analysis Seminar, Courant Institute for the Mathematical Sciences, New York University, \(L^1\) Estimates for vector fields.
5 avril 2005
Groupe de travail – analyse non linéaire, Laboratoire J.-L. Lions, Université de Paris 6, Estimations \(L^1\) pour des champs de vecteurs.
20–22 mai 2005
Joint BeNeLuxFra conference in Mathematics, Gand, Belgique, \(L^1\) Estimates for vector fields.
24 mai 2005
Oberseminar Analysis, Max Planck Institute for Mathematics in the Sciences, Leipzig, Allemagne, \(L^1\) Estimates for vector fields.
26 juin 2005–2 juillet 2005
Topological and Variational Methods for Differential Equations, Mathematisches Forschungsinstitut Oberwolfach, Allemagne, Symmetrization and symmetry of critical points.
1ᵉʳ–5 août 2005
Fixed Point Theory and its Applications, Będlewo, Pologne, Symmetry properties of solutions of semilinear elliptic problems.
12 septembre 2005
PhD Day, Belgian Mathematical Society, Bruxelles, Approximation of symmetrizations and symmetry of critical points.
15 décembre 2005
Séminaire d’analyse, Tours, France, Réarrangement symétrique: approximation et symétrie de points critiques.
15 février 2006
Groupe de travail –analyse non linéaire, Laboratoire J.-L. Lions, Université de Paris 6, États stationnaires pour l’équation de Schrödinger non linéaire dans le cas semi-classique.
5 mai 2006
Séminaire “Équations aux dérivées partielles et applications”, Collège de France, Paris, France, Estimations pour des systèmes elliptiques à données \(L^1\).
22 mai 2006
Séminaire “Équations aux Dérivées Partielles”, Institut Camille Jordan, Université de Lyon I, France, Estimations pour des systèmes elliptiques à données \(L^1\).
6 novembre 2006
Oberseminar Analysis Mathematisches Institut, Universität zu Köln, Cologne, Allemagne, Approximation of symmetrizations by polarizations and symmetry of solutions of elliptic problems .
14 novembre 2006
Analysis and Partial Differential Equations Seminar, Department of Mathematics, University of Bristol, Royaume-Uni, \(L^1\) estimates for vector fields.
29 novembre 2006
Rutgers analysis seminar, Rutgers University, New Brunswick, New Jersey, États-Unis d’Amérique, \(L^1\) estimates for vector fields.
3–10 juin 2007
Geometric Analysis and Nonlinear Partial Differential Equations, Będlewo, Pologne, Estimates for \(L^1\) vector fields.
15 janvier 2008
Rutgers analysis seminar, Rutgers University, New Brunswick, New Jersey, États-Unis d’Amérique, Desingularization of vortices for the Euler equation by a semilinear elliptic problem.
11–12 février 2008
Seminar on Analysis, Institut für Mathematik, RWTH Aachen, Aix-la-Chapelle, Allemagne, Desingularization of vortices for the Euler equation by a semilinear elliptic problem.
10 avril 2008
Mathematisches Institut, Justus Liebig Universität Gießen, Allemagne, Desingularization of vortices for the Euler equation by a semilinear elliptic problem.
15 mai 2008
Seminarium Zakładu Równań Fizyki Matematycznej, Wydział Matematiky, Informatyki i Mechaniki, Uniwersytet Warszawski, Varsovie, Pologne, Estimates for \(L^1\) vector-fields.
4 juin 2008
Colloquium, Centre for Analysis, Scientific computing and Applications, Technische Universiteit Eindhoven, Pays-Bas, Semilinear elliptic problems and vortices for the Euler equation.
17 juin 2008
SFB Seminar, Institut für Angewandte Mathematik, Universität Bonn, Estimates for \(L^1\) vector-fields.
3–4 juillet 2008
Four Generations under One Roof, A workshop in nonlinear analysis, Université de Paris 6, Semilinear elliptic problems and vortices for the Euler equation.
15 janvier 2009
Analysis and PDEs Seminar, Swansea University, Pays de Galles, Royaume-Uni, Desingularisation of vortices for the Euler equation by a semilinear elliptic problem.
11 février 2009
Nonlinear Analysis and PDEs Seminar, Rutgers University, Semiclassical stationary states for the nonlinear Schrödinger equations with fast decaying potentials.
2 avril 2009
Seminario di Analisi, Dipartimento di Matematica “Ulisse Dini” Universitá degli Studi di Firenze, Estimates for \(L^1\) vector fields.
16 juillet 2009
CASA Minimsymposium on Special limits in PDEs Technische Universiteit Eindhoven, Pays-Bas, Periodic homogenization, convergence of monotone operators and Mosco convergence.
15-16 janvier 2009
Second South West Regional PDE Winter School, Swansea University, Pays de Galles, Royaume-Uni, Limiting estimates for \(L^1\) vector fields.
22 février 2010
Oberseminar Geometrische Analysis, Goethe Universität Frankfurt, Francfort, Allemagne, Existence of optimal functions for Poincaré-Sobolev inequalities.
3 juin 2010
ERC Nonlinear Problems in PDEs, Università degli Studi di Parma, What can be estimated by \(L^1\) norms of some derivatives of a vector field?
17 juin 2010
Analysis and PDEs Seminar, Swansea University, Pays de Galles, Royaume-Uni, Semiclassical stationary states for nonlinear Schroedinger equations with fast decaying potentials.
14-17 septembre 2010
4th Group Actions in Topology and Analysis Conference, Milan 2010, Approximation of symmetrizations.
26 janvier 2011
Nonlinear analysis seminar, Rutgers University, New Brunswick, New Jersey, États-Unis d’Amérique, Nonexistence of positive supersolutions for semilinear elliptic problems with a nonlocal nonlinearity.
23 février 2011
Seminario di Analisi Matematica, Sapienza Università di Roma, What can be estimated by the \(L^1\) norm of some components of the derivatives of a vector field?
7-8 juillet 2011
Seminar on Analysis, Institut für Mathematik, RWTH Aachen, Aix-la-Chapelle, Allemagne, What can be estimated by the \(L^1\) norm of some components of the derivatives of a vector field?
13-15 décembre 2011
Initial Training Network FRonts and Interfaces in Science and Technology (FIRST), Bath, Royaume-Uni, Nonexistence of positive super solutions for semilinear elliptic problems with a nonlocal nonlinearity.
15 décembre 2011
Analysis and PDEs Seminar, Swansea University, Nonexistence of positive super solutions for semilinear elliptic problems with a nonlocal nonlinearity.
4–7 septembre 2012
Meeting on Applied Mathematics and Calculus of Variations, Rome, Strong density for higher order Sobolev spaces into compact manifolds.
22 novembre 2012
Analysis and PDEs Seminar, Swansea University, Pays de Galles, Royaume-Uni, Density of smooth maps in higher order Sobolev spaces with values in manifolds.
12–14 décembre 2012
Workshop on Nonlocal Problems, Initial Training Network FRonts and Interfaces in Science and Technology (FIRST) Zürich, Suisse, Existence of groundstates for a class of nonlinear Choquard equations.
6–7 mars 2013
Nonlinear PDE Days (Frankfurt–Gießen–Karlsruhe–Köln), Universität Frankfurt, Francfort, Allemagne, Desingularization of stationary shallow water vortices
19 avril 2013
Séminaire - Analyse non linéaire et EDP, Université libre de Bruxelles, Existence et nonexistence de solutions pour des équations de Choquard
30 mai 2013
Analysis and PDEs Seminar, Swansea University, Pays de Galles, Royaume-Uni, Which differential operators on vector fields can appear in \(L^1\) Hardy and Sobolev inequalities?
7–10 janvier 2014
Variational Methods in Elliptic Equations and Systems, Workshop in the memory of Miguel Ramos, Universidade de Lisboa, Lisbonne, Portugal, Semi-classical states for the Choquard equation.
12 mai 2014
Partial Differential Equations Seminar, University of Oxford, Desingularization of stationary shallow water vortices.
15 mai 2014
Analysis and PDEs Seminar, Swansea University, Pays de Galles, Royaume-Uni, Semi-classical states for the Choquard equation.
30 juin-4 juillet 2014
Partial differential equations and nonlinearities, A conference in honor of Haïm Brezis, Paris, Lifting in Sobolev spaces revisited.
2 décembre 2014
Seminario di Matematica, Dipartimento di Matematica, Politecnico di Bari, Semi-classical states for the Choquard equation.
9 mars 2015
Séminaire de Physique Mathématique, Université de Grenoble, Désingularisation de tourbillons pour l’équation des lacs.
7–11 septembre 2015
Workshop in Nonlinear PDEs, Université Libre de Bruxelles, Nonlinear Schrödinger equation under a magnetic field kept in the foreground.
3 novembre 2015
Seminario de Ecuaciones Diferenciales, Universidad di Granada, Nodal solutions for the Choquard equation.
16 novembre 2015
Groupe de Travail Calcul des Variations, Laboratoire de Mathématiques, Université Paris-Sud (Orsay), Approximation d’applications Sobolev à valeur dans des variétés riemanniennes complètes.
16 novembre 2015
Séminaire de l’équipe équations aux dérivées partielles, Institut de recherche mathématique de Rennes, Université de Rennes 1, L'équation de Schrödinger non linéaire quand le champ magnétique est à l’avant-plan.
30 mai–3 juin 2016
Workshop on Nonlinear PDEs and Calculus of Variations, Chern Institute of Mathematics, Nankai University (香港中文大學), Tianjin, Chine, Symmetry of groundstates of some magnetic nonlinear Schrödinger equation and of least action nodal solutions to some Choquard equations.
4 juin 2016
Tianjin University (天津大学), Chine, Nodal solutions for the Choquard equation.
3 août 2016
Godeaux Lecture (Belgian Mathematical Society) and Brussels Summer School of Mathematics, Brussels, Belgique, Sobolev mappings: from liquid crystals to irrigation via degree theory.
12–16 septembre 2016
Partial Differential Equations and Related Topics, Alghero, Italie, Symmetry of groundstates of some magnetic nonlinear Schrödinger equation and of least action nodal solutions to some Choquard equations.
29 octobre 2016
Nonlinear PDE, Inequalities and Applications, Riemann International School of Mathematics Varese, Italie, Nodal solutions for the Choquard equation and their odd symmetry.
28 novembre 2016
Department of Mathematics, The Chinese University of Hong Kong (香港中文大學), Approximation by bounded mappings of Sobolev mappings into complete manifolds.
21 mars 2017
Séminaire d’analyse harmonique, Département de Mathématiques d’Orsay, Paris, France, Extension singulière contrôlée d’applications Sobolev.
1er juin 2017
Kandidatenseminar Analysis, Justus Liebig Universität Gießen, Mathematisches Institut, Nodal solutions for the Choquard equation and their odd symmetry.
12–16 juin 2017
23rd Rolf Nevanlinna Colloquium, ETH Zürich, Forschungsinstitut für Mathematik, Uniform boundedness principle for Sobolev maps between manifolds.
4–7 octobre 2017
Workshop on Analysis and PDE, Leibniz Universität Hannover, The Choquard equation under a logarithmic potential.
20 novembre 2017
Universitatea din Bucuresti, Facultatea de Matematica si Informatica, Seminar de analiză și EDP,\(L^1\) estimates and canceling conditions.
22 novembre 2017
Institutul de Matematică “Simion Stoilow” al Academiei Române, IMAR Monthly lecture, Is symmetry better? Symmetry and symmetry breaking arising in calculus of variations and partial differential equations.
4 décembre 2017
Università di Roma “La Sapienza”, Seminario di Analisi Matematica, Uniform boundedness principle for Sobolev maps between manifolds.
13 mars 2018
Department of Mathematics, The Chinese University of Hong Kong, Uniform boundedness principle for Sobolev maps between manifolds.
15 mars 2018
Hong Kong University of Science and Technology, Seminar on PDE, Limiting Sobolev estimates for vector fields and canceling differential operators.
15 juin 2018
Journée d’analyse et équations aux dérivées partielles, Bruxelles, Lifting fractional Sobolev maps over a compact covering.
18–22 juin 2018
Analysis of singular patterns in variational models, Toulouse, Lifting fractional Sobolev maps over a compact covering.
2–4 juillet 2018
International Workshop on Critical Phenomena, National Chiao Tung University, Hsinchu, Taiwan, Limiting Sobolev estimates for vector fields and canceling differential operators.
5–9 juillet 2018
The 12th AIMS Conference on Dynamical Systems, Differential Equations and Applications, Taipei, Taiwan, The Choquard Equation Under a Logarithmic Potential.
16–19 juillet 2018
Variational Problems arising from Physics and Geometry, On the occasion of the 60th birthday of Thomas Bartsch, Rauischholzhausen (Allemagne), Vortex dynamics for the lake equation.
23–27 juillet 2018
Geometric PDEs in Freiburg 2018, Fribourg en Brigau(Allemagne), Uniform boundedness principle for Sobolev maps between manifolds.
21 septembre 2018
Séminaire d’analyse, École Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Suisse, Critical estimates on the homotopy of maps between manifolds.
30 octobre 2018
Nonlinear Analysis and PDE Seminar, Rutgers University, États-Unis d’Amérique, Endpoint estimates in Lorentz spaces for vector fields.
9 novembre 2018
Colloquium, Department of Mathematics, University of Pittsburgh, États Unis d’Amérique, Endpoint Sobolev inequalities for vector fields.
5 décembre 2018
Recent breakthroughs in Mathematics, Belgian Mathematical Society, Bruxelles, Belgique, about optimal transport, PDEs and Alessio Figalli's Fields medal in 2018.
11 février 2019
Partial Differential Equations Seminar, University of Oxford, Royaume-Uni, Ginzburg–Landau functionals with a general compact vacuum manifold on planar domains.
18 février 2019
Analysis and PDEs seminar, Swansea University, Royaume-Uni, Vortex dynamics for the lake equations.
20 février 2019
Partial Differential Equations and their Applications Seminar, University of Warwick, Coventry, Royaume-Uni, Endpoint estimates in Lorentz spaces for vector fields.
13–17 mai 2019
Analytic-Geometric Inequalities and Related Topics, Institut Mittag-Leffler, The Royal Sweedish Academy of SciencesStockholm, Suède, “Limiting Sobolev estimates for vector fields and canceling differential operators”.
20–24 mai 2019
Workshop on variational problems in physics, Centre international de Mathématiques et d’Informatique de Toulouse, Toulouse, France, “Ginzburg–Landau functionals for a general compact vacuum manifold on planar domains”.
2–6 juin 2019
New Perspectives in nonlinear PDE: A research workshop in honor of Prof. Haim Brezis, Department of Mathematics, Technion, Haïfa, Israël, “Estimates for the Hopf invariant in critical fractional Sobolev spaces”.
9–11 septembre 2019
Regularity aspects of linear growth functionals, Institute for Mathematics, University of Augsburg, Augsbourg, Allemagne, “Endpoint estimates in Lorentz spaces for vector fields”.
31 octobre 2019
Bourgain Day, Paleis der Academiën, Bruxelles, Belgique, “Sobolev topology, Ginzburg-Landau energy and elliptic systems regularity”.
28 janvier 2020
Rutgers analysis seminar, Rutgers University, New Brunswick, New Jersey, “Ginzburg-Landau functionals for a general compact vacuum manifold on planar domains”.
11 juin 2020
Corona seminar: Inequalities on Function Spaces of Smooth Functionsen ligne, “Marcinkiewicz meets Gagliardo and Sobolev: weak-type formulas for norms of the gradient”.
2–6 novembre 2020
Workshop on Vortex Filaments, Fields Institute, Toronto, Canada (en ligne), “Vortex dynamics for the lake equations”.
1–3 février 2021
ICMC Summer Meeting on Differential Equations – 2021 Chapter, Universidade de São Paulo, Instituto de Ciências Matemáticas e de Computação, São Carlos, Brésil (en ligne), “Ginzburg–Landau functionals for a general compact vacuum manifold on planar domains”.
9 février 2021
Learning Seminar on PDE and Applications, Rutgers University, New Brunswick, États-Unis d’Amérique (en ligne), “Marcinkiewicz–Gagliardo weak-type formulas for Sobolev norms”.
22 avril 2021
Nonlinear Analysis Seminar Series, Okinawa Institute of Science and Technology (沖縄科学技術大学院大学), Okinawa, Japon (en ligne), “Vortex dynamics for the lake equations”.
7–11 juin 2021
Canadian Mathematical Society 75+1 Anniversary meeting, Harmonic Analysis and Partial Differential Equations session, Toronto (Canada), (en ligne), “Marcinkiewicz meets Gagliardo and Sobolev: weak-type formulas for norms of the gradient”.
20–26 juin 2021
8th European Congress of Mathematics, Geometric-functional inequalities and related topics session, Portorož, Slovénie (en ligne), “Reverse superposition estimates, lifting over a compact covering and extensions of traces for fractional Sobolev mappings”.
5–10 septembre 2021
Nonlinear Potential Theoretic Methods in Partial Differential Equations, Banff International Research station, Alberta, Canada (en ligne), “Ginzburg–Landau functionals on planar domains for a general compact vacuum manifold”.
17–23 octobre 2021
Rajchman, Zygmund, Marcinkiewicz conference, Varsovie, Pologne (en ligne), “Marcinkiewicz meets Gagliardo and Sobolev: getting weak differentiability from weak-type estimates”.
20 avril 2022
Webinar in Analysis and Differential Equations (CAMGSD, CMAFcIO & GFM), Lisbonne, Portugal (en ligne), “Ginzburg-Landau functionals on planar domains for a general compact vacuum manifold”.
3 juin 2022
Zhejiang UniversityHangzhou, Chine (en ligne), “Ginzburg-Landau functionals on planar domains for a general compact vacuum manifold”.
9 juin 2022
Energy, Entropy, and Dissipative Dynamics (EDDY) seminar, RWTH, Aix-la-Chapelle, Allemagne), “Ginzburg-Landau functionals on planar domains for a general compact vacuum manifold”.
4 juillet 2022
Università di Roma “La Sapienza”, Seminario di Analisi Matematica, Ginzburg--Landau functionals on planar domains for a general compact vacuum manifold.
26 octobre 2022
Universiteit Gent (UGent), Ghent Methusalem Colloquium, Endpoint Sobolev inequalities for vector fields and cancelling operators.
17 novembre 2022
Analysis seminar, Universität Duisburg–Essen, Essen, Limiting Sobolev estimates for vector fields and cancelling differential operators.
4–6 octobre 2023
Conference on Trends in Analysis 2023, Universität Duisburg–Essen, Duisburg, \(p \nearrow 2\)–harmonic maps on three-dimensional domains.

Cours avancés

22–24 janvier 2013
Universitá di Pisa, Dipartimento di Matematica, minicours de 6h : “Symmetrization and symmetry properties of solutions to variational problems”
18 janvier–8 mars 2019
University of Oxford, Mathematical Institute, Cours de 16h : “Sobolev mappings into manifolds”
28–31 mars 2019
VIIth Spring School of Analysis in memory of Aleksander Pełczyński: Differentiation and Geometry, Institute of Mathematics of the Polish Academy of Sciences, Banach center, Będlewo, (Pologne), minicours de 6h : “Endpoint Sobolev estimates for vector fields and canceling differential operators”.
27 juin–1ᵉʳ juillet 2022
Geometric and analytic aspects of functional variational principles, Centro Internazionale Matematico Estivo (CIME), (Cetraro, Cosenza, Italie), minicours de 4h : “Limiting Sobolev estimates for vector fields and canceling dfferential operators”.
28 mai–3 juin 2023
Function Spaces and Applications XII, Faculty of Mathematics and Physics of Charles University and Faculty of Electrical Engineering of the Czech Technical University in Prague (Paseky nad Jizerou, République tchèque), minicours de 5h : “Limiting Sobolev estimates for vector fields and cancelling differential operators”.

Assistance à des conférences

22 avril 2003–9 mai 2003
Workshop and Conference on Recent Trends in Nonlinear Variational Problems, Abdus Salam International Centre for Theoretical Physics, Trieste, Italie
21–25 juin 2004
Nonlinear Analysis — Conference in Honor of Haïm Brezis, Paris, France.
2–8 juillet 2006
Global and Geometric Aspects of Nonlinear Partial Differential Equations, European Science Foundation Programme, Évolène, Valais, Suisse.
26–30 avril 2010
Differential and topological problems in modern theoretical physics, SISSA, Trieste, Italie.
24–30 juillet 2012
Calculus of variations, Oberwolfach, Allemagne.

Encadrement de doctorats

Thèses promues

2007–2011
Jonathan Di Cosmo, Nonlinear Schrödinger equation and Schrödinger–Poisson system in the semiclassical limit, (copromoteur : Denis Bonheure, Université Libre de Bruxelles).
2011–2017
Alexandra Convent, Intrinsinc Sobolev maps between manifolds.
2014–2019
Justin Dekeyser, Equimeasurable functions and their application to vortex dynamics in lakes.

Thèses en cours

2021–
Benoît Van Vaerenbergh, Relaxation \(p\)-harmonique d’applications harmoniques singulières renormalisables.

Encadrement informel

2015–2016
Xia Jiankang (夏健康), Choquard equation: coercive potentials and critical frequency problem.

Encadrement de post-doctorants

2015–2016
Luca Battaglia.
2016–2019
Antonin Monteil.
2017–2019
Rémy Rodiac.
2018–2021
Katarzyna Mazowiecka.
2021–2023
Bohdan Bulanyi.
2021–2024
Adolfo Arroyo-Rabasa.

Responsabilités éditoriales

2012–2020
Advances in Nonlinear Analysis, De Gruyter.
2015–
Journal of Fixed Point Theory and its Applications, Birkhäuser, section editor.

Responsabilités de financement de la recherche

2016–2021
Membre du jury FRIA (président de 2019 à 2021)
2021–
Membre de commission scientifique du Fonds de la Recherche Scientifique–FNRS.

Organisation de colloques

26–30 mai 2008
Spring school in nonlinear partial differential equations, Louvain-la-Neuve, partiellement financée par le réseau GLOBAL de l’European Science Foundation (comité d’organisation).
10–12 septembre 2008
Nonlinear Differential Equations, Académie Royale de Belgique, Bruxelles (comité d’organisation).
2–4 septembre 2009
Workshop on Nonlinear Elliptic PDEs, ULB, Bruxelles (comité scientifique).
17–21 mai 2010
Spring School in Nonlinear Partial Differential Equations, Bruxelles.
27–29 juin 2011
Workshop on singular reaction-diffusion, Louvain-la-Neuve.
30 mai – 6 juin 2012
Spring School in Nonlinear Partial Differential Equations, Bruxelles.
11–12 juillet 2013
Workshop on Variational methods and partial differential equations, Louvain-la-Neuve.
14–18 décembre 2015
École d’hiver « Nonlinear Function Spaces in Mathematics and Physical Sciences », Lyon.
13–17 novembre 2017
First Belgium–Chile–Italy conference in PDEs, Université libre de Bruxelles.