Jean Van Schaftingen

# Publications

## Submitted papers

[1] , , , and , Spaces of Besov–Sobolev type and a problem on nonlinear approximation.

[2] , , and , Families of functionals representing Sobolev norms.

[3] and , Limiting Sobolev and Hardy inequalities on stratified homogeneous groups.

## Accepted papers

[4] and , Quantitative characterization of traces of Sobolev maps, to appear in Commun. Contemp. Math.

[5] , and , Renormalised energies and renormalisable singular harmonic maps into a compact manifold on planar domains, to appear in Math. Annal.

[6] , Reverse superposition estimates in Sobolev spaces, to appear in Pure Appl. Funct. Anal.

## Published papers

[7] , and , On limiting trace inequalities for vectorial differential operators, Indiana Univ. Math. J. 70 (2021), no. 5, 2133–2176.

[8] , and , Ginzburg-Landau relaxation for harmonic maps on planar domains into a general compact vacuum manifold, Arch. Rat. Mech. Anal. 242 (2021), no. 2, 875–935.

[9] and , Lifting in compact covering spaces for fractional Sobolev mappings, Anal. PDE 14 (2021), no. 6, 1851–1871.

[10] and , Trace theory for Sobolev mappings into a manifold, Ann. Fac. Sci. Toulouse Math. (6) 30 (2021), no. 2, 281–299.

[11] , and , Going to Lorentz when fractional Sobolev, Gagliardo and Nirenberg estimates fail, Calc. Var. Partial Differential Equations 60 (2021), no. 129

[12] , and , A surprising formula for Sobolev norms, Proc. Natl. Acad. Sci. USA 118 (2021), no. 8, e2025254118.

[13] and , Metric characterization of the sum of fractional Sobolev spaces, Stud. Math. 258 (2021), 27–51.

[14] and , Estimates of the amplitude of holonomies by the curvature of a connection on a bundle, Pure Appl. Funct. Anal. 5 (2020), no. 4, 891–897.

[15] and , Characterization of the traces on the boundary of functions in magnetic Sobolev spaces, Adv. Math. 371 (2020), 107246.

[16] , and , Groundstates for Choquard type equations with Hardy–Littlewood–Sobolev lower critical exponent, Proc. Roy. Soc. Edinb. A 150 (2020), no. 3, 1377–1400.

[17] and , Range convergence monotonicity for vector measures and range monotonicity of the mass, Ric. Mat. 69 (2020), no. 1, 293-326.

[18] and , An estimate of the Hopf degree of fractional Sobolev mappings, Proc. Amer. Math. Soc. 148 (2020), no. 7, 2877–2891.

[19] and , Vortex motion for the lake equations, Comm. Math. Phys. 375 (2020), no. 2, 1459–1501.

[20] , Estimates by gap potentials of free homotopy decompositions of critical Sobolev maps, Adv. Nonlinear Anal. 9 (2019), no. 1, 1214–1250.

[21] and , Optimal embeddings into Lorentz spaces for some vector differential operators via Gagliardo’s lemma, Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 30 (2019), no. 3, 413–436.

[22] , , and , Representing three-dimensional cross fields using fourth order tensors, in Roca  X. and Loseille  A. (eds.), 27th International Meshing Roundtable. IMR 2018, Springer, Cham, Lecture Notes in Computational Science and Engineering, No. 127, 2019, 89–108.

[23] and , Higher order intrinsic weak differentiability and Sobolev spaces between manifolds, Adv. Calc. Var. 12 (2019), no. 3, 303–332.

[24] , and , Properties of groundstates of nonlinear Schrödinger equations under a weak constant magnetic field, J. Math. Pures Appl. (9) 124 (2019), 123–168.

[25] and , Uniform boundedness principles for Sobolev maps into manifolds, Ann. Inst. H. Poincaré Anal. Non Linéaire 36 (2019), no. 2, 417–449.

[26] , , , and , Sharp Gagliardo-Nirenberg inequalities in fractional Coulomb–Sobolev spaces, Trans. Amer. Math. Soc. 370 (2018), no. 11, 8285–8310.

[27] and , Groundstates of the Choquard equations with a sign-changing self-interaction potential, Z. Angew. Math. Phys. 69 (2018), no. 3, 69:86.

[28] and , Groundstates for a local nonlinear perturbation of the Choquard equations with lower critical exponent, J. Math. Anal. Appl. 464 (2018), no. 2, 1184–1202.

[29] , and , Weak approximation by bounded Sobolev maps with values into complete manifolds, C. R. Math. Acad. Sci. Paris 356 (2018), no. 3, 264–271.

[30] , 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)

[31] and , Odd symmetry of least energy nodal solutions for the Choquard equation, J. Differential Equations 264 (2018), no. 2, 1231–1262.

[32] and , Gauge-measurable functions, Rend. Istit. Mat. Univ. Trieste 49 (2017), 113–135.

[33] , , and , Semiclassical Sobolev constants for the electro-magnetic Robin Laplacian, J. Math. Soc. Japan 69 (2017), no. 4, 1667–1714.

[34] , and , Density of bounded maps in Sobolev spaces into complete manifolds, Ann. Mat. Pura Appl. (4) 196 (2017), no. 6, 2261–2301.

[35] and , Approximation of symmetrizations by Markov processes, Indiana Univ. Math. J. 66 (2017), no. 4, 1145–1172.

[36] and , Standing waves with a critical frequency for nonlinear Choquard equations, Nonlinear Anal. 161 (2017), 87–107.

[37] , and , The logarithmic Choquard equation: sharp asymptotics and nondegeneracy of the groundstate, J. Funct. Anal. 272 (2017), no. 12, 5255–5281.

[38] , and , Bourgain–Brezis estimates on symmetric spaces of non-compact type, J. Funct. Anal. 273 (2017), no. 4, 1504-1547.

[39] and , Existence of groundstates for a class of nonlinear Choquard equations in the plane, Adv. Nonlinear Stud. 17 (2017), no. 3, 581–594.

[40] , and , The incompressible Navier Stokes flow in two dimensions with prescribed vorticity, in Sagun  Chanillo, Bruno  Franchi, Guozhen  Lu, Carlos  Perez and Eric T.  Sawyer (eds.), Harmonic Analysis, Partial Differential Equations and Applications, Birkhäuser, Applied and Numerical Harmonic Analysis, 2017, 19–25.

[41] and , Controlled singular extension of critical trace Sobolev maps from spheres to compact manifolds, Int. Math. Res. Not. IMRN 2017 (2017), no. 12, 3467–3683.

[42] and , A guide to the Choquard equation, J. Fixed Point Theory Appl. 19 (2017), no. 1, 773–813.

[43] , and , An $$L^1$$–type estimate for Riesz potentials, Rev. Mat. Iberoam. 33 (2017), no. 1, 291–304.

[44] , and , Variations on a proof of a borderline Bourgain–Brezis Sobolev embedding theorem, Chinese Ann. Math. Ser. B 38 (2017), no. 1, 235–252.

[45] and , Choquard equations under confining external potentials, NoDEA Nonlinear Differential Equations Appl. 24 (2017), no. 1, 1–24.

[46] , and , Least action nodal solutions for the quadratic Choquard equation, Proc. Amer. Math. Soc. 145 (2017), no. 2, 737–747.

[47] , and , Groundstates and radial solutions to nonlinear Schrödinger–Poisson–Slater equations at the critical frequency, Calc. Var. Partial Differential Equations 55 (2016), no. 146, 58.

[48] and , Nodal solutions for the Choquard equation, J. Funct. Anal. 271 (2016), no. 1, 107–135.

[49] and , Intrinsic colocal weak derivatives and Sobolev spaces between manifolds, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 16 (2016), no. 1, 97–128.

[50] , and , Applications of Bourgain–Brezis inequalities to fluid mechanics and magnetism, C. R. Math. Acad. Sci. Paris 354 (2016), no. 1, 51–55.

[51] and , Geometric partial differentiability on manifolds: the tangential derivative and the chain rule, J. Math. Anal. Appl. 435 (2016), no. 2, 1672–1681.

[52] and , Groundstates of nonlinear Choquard equations: Hardy–Littlewood–Sobolev critical exponent, Commun. Contemp. Math. 17 (2015), no. 5, 1550005 (12 pages).

[53] and , Existence of groundstates for a class of nonlinear Choquard equations, Trans. Amer. Math. Soc. 367 (2015), no. 9, 6557–6579.

[54] and , Semiclassical stationary states for nonlinear Schrödinger equations under a strong external magnetic field, J. Differential Equations 259 (2015), no. 2, 596–627.

[55] , and , Strong density for higher order Sobolev spaces into compact manifolds, J. Eur. Math. Soc. (JEMS) 17 (2015), no. 4, 763–817.

[56] and , Semi-classical states for the Choquard equations, Calc. Var. Partial Differential Equations 52 (2015), no. 1, 199–235.

[57] and , 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), no. 1, 255–271.

[58] , Limiting Bourgain–Brezis estimates for systems of linear differential equations: Theme and variations, J. Fixed Point Theory Appl. 15 (2014), no. 2, 273–297.

[59] , and , Strong approximation of fractional Sobolev maps, J. Fixed Point Theory Appl. 15 (2014), no. 1, 133–153.

[60] and , Hardy–Sobolev inequalities for vector fields and canceling linear differential operators, Indiana Univ. Math. J. 63 (2014), no. 5, 1419–1445.

[61] , Equivalence between Pólya–Szegő and relative capacity inequalities under rearrangement, Arch. Math. (Basel) 103 (2014), no. 4, 367–379.

[62] , Interpolation inequalities between Sobolev and Morrey–Campanato spaces: A common gateway to concentration-compactness and Gagliardo–Nirenberg, Port. Math. 71 (2014), no. 3–4, 159–175.

[63] , Approximation in Sobolev spaces by piecewise affine interpolation, J. Math. Anal. Appl. 420 (2014), no. 1, 40–47.

[64] , and , Density of smooth maps for fractional Sobolev spaces $$W^{s, p}$$ into $$\ell$$–simply connected manifolds when $$s \ge 1$$, Confluentes Math. 5 (2013), no. 2, 3–22.

[65] and , Desingularization of vortex rings and shallow water vortices by a semilinear elliptic problem, Arch. Rat. Mech. Anal. 210 (2013), no. 2, 409–450.

[66] , A direct proof of the existence of eigenvalues and eigenvectors by Weierstrass’s theorem, Amer. Math. Monthly 120 (2013), no. 8, 741–746.

[67] and , Groundstates of nonlinear Choquard equations: existence, qualitative properties and decay asymptotics, J. Funct. Anal. 265 (2013), no. 2, 153–184.

[68] and , Stationary solutions of the nonlinear Schrödinger equation with fast-decay potentials concentrating around local maxima, Calc. Var. Partial Differential Equations 47 (2013), no. 1–2, 243–271.

[69] , Limiting Sobolev inequalities for vector fields and canceling linear differential operators, J. Eur. Math. Soc. (JEMS) 15 (2013), no. 3, 877–921.

[70] and , Nonexistence and optimal decay of supersolutions to Choquard equations in exterior domains, J. Differential Equations 254 (2013), no. 8, 3089–3145.

[71] and , Nonlocal Hardy type inequalities with optimal constants and remainder terms, Ann. Univ. Buchar. Math. Ser. 3 (LXI) (2012), no. 2, 187–200.

[72] and , Finding critical points whose polarization is also a critical point, Topol. Methods Nonlinear Anal. 40 (2012), no. 2, 371–379.

[73] , and , Nonlinear Schrödinger equation with unbounded or vanishing potentials: solutions concentrating on lower dimensional spheres, J. Differential Equations 252 (2012), no. 1, 941–968.

[74] and , 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 and Michel  Willem (eds.), Nonlinear Elliptic Partial Differential Equations, Amer. Math. Soc., Contemporary Mathematics, No. 540, 2011, 47–58.

[75] and , Desingularization of vortices for the Euler equation, Arch. Rat. Mech. Anal. 198 (2010), no. 3, 869–925.

[76] and , Groundstates for the nonlinear Schrödinger equation with potential vanishing at infinity, Ann. Mat. Pura Appl. (4) 189 (2010), 273–301.

[77] and , Semiclassical stationary states for nonlinear Schrödinger equations with fast decaying potentials, Calc. Var. Partial Differential Equations 37 (2010), no. 1, 1—27.

[78] , Limiting fractional and Lorentz spaces estimates of differential forms, Proc. Amer. Math. Soc. 138 (2010), no. 1, 235–240.

[79] and , Closure of Smooth Maps in $$W^{1,p}(B^3;S^2)$$, Differential Integral Equations 22 (2009), no. 9–10, 881–900.

[80] , Explicit approximation of the symmetric rearrangement by polarizations, Arch. Math. (Basel) 93 (2009), no. 2, 181–190.

[81] and , Existence and concentration for nonlinear Schrödinger equations with fast decaying potentials, C. R. Math. Acad. Sci. Paris 347 (2009), no. 15–16, 921–926.

[82] , and , Pathological solutions to elliptic problems in divergence form with continuous coefficients, C. R. Math. Acad. Sci. Paris 347 (2009), no. 13–14, 773–778.

[83] and , Subelliptic Bourgain–Brezis estimates on groups, Math. Res. Lett. 16 (2009), no. 3, 487–501.

[84] and , Circulation integrals and critical Sobolev spaces: problems of optimal constants, in Dorina  Mitrea and Marius  Mitrea (eds.), Perspectives in Partial Differential Equations, Harmonic Analysis and Applications, Amer. Math. Soc., Proc. Sympos. Pure Math., No. 79, 2008, 33–47.

[85] , and , Periodic homogenization for convex functionals using Mosco convergence, Ricerche Mat. 57 (2008), no. 2, 209–249.

[86] , Estimates for $$\mathrm{L}^1$$ vector fields under higher-order differential conditions, J. Eur. Math. Soc. (JEMS) 10 (2008), no. 4, 867–882.

[87] , , and , Asymptotics and symmetries of least energy nodal solutions of Lane–Emden problems with slow growth, Commun. Contemp. Math. 10 (2008), no. 4, 609–631.

[88] , and , A case of density in $$W^{2,p}(M;N)$$, C. R. Math. Acad. Sci. Paris 346 (2008), no. 13–14, 735–740.

[89] and , Bound state solutions for a class of nonlinear Schrödinger equations, Rev. Mat. Iberoam. 24 (2008), no. 1, 297–351.

[90] and , Symmetry of solutions of semilinear elliptic problems, J. Eur. Math. Soc. (JEMS) 10 (2008), no. 2, 439–456.

[91] , and , Periodic homogenization of monotone multivalued operators, Nonlinear Anal. 67 (2007), no. 12, 3217–3239.

[92] and , Boundary estimates for elliptic systems with $$L^1$$–data, Calc. Var. Partial Differential Equations 30 (2007), no. 3, 369–388.

[93] and , The continuity of functions with $$N$$–th derivative measure, Houston J. Math. 33 (2007), no. 3, 927–939.

[94] , Approximation of symmetrizations and symmetry of critical points, Topol. Methods Nonlinear Anal. 28 (2006), no. 1, 61–85.

[95] , Anisotropic symmetrization, Ann. Inst. H. Poincaré Anal. Non Linéaire 23 (2006), no. 4, 539–565.

[96] , Function spaces between BMO and critical Sobolev spaces, J. Funct. Anal. 236 (2006), no. 2, 490–516.

[97] and , Nonlinear Schrödinger equations with potentials vanishing at infinity, C. R. Math. Acad. Sci. Paris 342 (2006), no. 12, 903–908.

[98] , Universal approximation of symmetrizations by polarizations, Proc. Amer. Math. Soc. 134 (2006), no. 1, 177–186.

[99] and , Periodic reiterated homogenization for elliptic functions, J. Math. Pures Appl. (9) 84 (2005), no. 12, 1716–1743.

[100] , Symmetrization and minimax principles, Commun. Contemp. Math. 7 (2005), no. 4, 463–481.

[101] and , Reiterated homogenization for elliptic operators, C. R. Math. Acad. Sci. Paris 340 (2005), no. 3, 209–214.

[102] , Estimates for $$L^1$$ vector fields with a second order condition, Acad. Roy. Belg. Bull. Cl. Sci. (6) 15 (2004), no. 1–6, 103–112.

[103] and , Set transformations, symmetrizations and isoperimetric inequalities, in V.  Benci and A.  Masiello (eds.), Nonlinear analysis and applications to physical sciences, Springer Italia, Milan, 2004, 135–152.

[104] , Estimates for $$L^1$$–vector fields, C. R. Math. Acad. Sci. Paris 339 (2004), no. 3, 181–186.

[105] , A simple proof of an inequality of Bourgain, Brezis and Mironescu, C. R. Math. Acad. Sci. Paris 338 (2004), no. 1, 23–26.

## Theses

[106] , Symmetrizations, Symmetry of Critical Points and $$L^1$$ Estimates, Thèse de doctorat, Université catholique de Louvain, Faculté des Sciences, 2005.

[107] , Symétrisations: mesure, géométrie et approximation, Travail de diplôme d’études approfondies, Université catholique de Louvain, Faculté des Sciences, 2003.

[108] , Symétrisation et problèmes elliptiques non linéaires, Travail de fin d’études, Université catholique de Louvain, Faculté des Sciences appliquées, 2002.

Last modification: 2022-01-12 17:25.