Augusto Ponce

Papers

• Density of smooth maps for fractional Sobolev spaces \(W^{s, p}\) into \(\ell\) simply connected manifolds when \(s \ge 1\)
  In collaboration with Pierre Bousquet and Jean Van Schaftingen
  Submitted paper.

• Limit solutions of the Chern-Simons equation
  In collaboration with Adilson E. Presoto
  Submitted paper.

• Nonexistence of solutions for the \(1\) Laplacian with \(L^N\) data
  In collaboration with Luigi Orsina
  Submitted paper.

• Singularities of the divergence of continuous vector fields and uniform Hausdorff estimates
  To appear in Indiana Univ. Math. J.

• Selected problems on elliptic equations involving measures
  Manuscript submitted to the concours annuel 2012 of the Académie royale de Belgique.

• Strong density for higher order Sobolev spaces into compact manifolds
  In collaboration with Pierre Bousquet and Jean Van Schaftingen
  Submitted paper.

• Diffuse measures and nonlinear parabolic equations
  In collaboration with Francesco Petitta and Alessio Porretta
  J. Evol. Eq. 11 (2011), 861–905.
  • These results have been announced in a note:
    Approximation of diffuse measures for parabolic capacities
    C. R. Acad. Sci. Paris, Ser. I 346 (2008), 161–166.

• Boundary singularities of positive solutions of some nonlinear elliptic equations
  In collaboration with Marie-Françoise Bidaut-Véron and Laurent Véron
  Calc. Var. Partial Differential Equations 40 (2011), 183–221.
  • These results have been announced in a note:
    Boundary singularities of positive solutions of some nonlinear elliptic equations
    C. R. Acad. Sci. Paris, Ser. I 344 (2007), 83–88.

• Reduced limits for nonlinear equations with measures
  In collaboration with Moshe Marcus
  J. Funct. Anal. 258 (2010), 2316–2372.

• A case of density in \(W^{2, p}(M; N)\)
  In collaboration with Pierre Bousquet and Jean Van Schaftingen
  C. R. Acad. Sci. Paris, Ser. I 346 (2008), 735–740.

• Closure of smooth maps in \(W^{1, p}(B^3; S^2)\)
  In collaboration with Jean Van Schaftingen
  Diff. Int. Equ. 22 (2009), 881–900.

• Semilinear elliptic equations and systems with diffuse measures
  In collaboration with Luigi Orsina
  J. Evol. Equ. 8 (2008), 781–812.

• Kato's inequality up to the boundary
  In collaboration with Haïm Brezis
  Comm. Contemp. Math. 10 (2008), 1217–1241.

• Hausdorff dimension of rupture sets and removable singularities
  In collaboration with Juan Dávila
  C. R. Acad. Sci. Paris, Ser. I 346 (2008), 27–32.

• A system of elliptic equations arising in Chern-Simons field theory
  In collaboration with Chang-Shou Lin and Yisong Yang
  J. Funct. Anal. 247 (2007), 289–350.

• The sub-supersolution method for weak solutions
  In collaboration with Marcelo Montenegro
  Proc. Amer. Math. Soc. 136 (2008), 2429–2438.

• The continuity of functions with N-th derivative measure
  In collaboration with Jean Van Schaftingen
  Houston J. Math. 33 (2007), 927–938.

• Reduced measures for obstacle problems
  In collaboration with Haïm Brezis
  Adv. Diff. Eq. 10 (2005), 1201–1234.

• Elliptic equations with vertical asymptotes in the nonlinear term
  In collaboration with Louis Dupaigne and Alessio Porretta
  J. Anal. Math. 98 (2006), 349–396.

• Reduced measures on the boundary
  In collaboration with Haïm Brezis
  J. Funct. Anal. 229 (2005), 95–120.

• How to construct good measures
  Elliptic and parabolic problems
  (C. Bandle, H. Berestycki, B. Brighi, A. Brillard, M. Chipot, J.-M. Coron,
  C. Sbordone, I. Shafrir, V. Valente and G. Vergara-Caffarelli, eds.),
  Progress in Nonlinear Differential Equations and their Applications, 63.
  Birkhäuser, Verlag Basel, 2005, pp. 335–348.
  A special tribute to the work of Haïm Brezis.

• Semilinear equations with exponential nonlinearity and measure data
  In collaboration with Daniele Bartolucci, Fabiana Leoni and Luigi Orsina
  Ann. Inst. H. Poincaré Anal. Non Linéaire 22 (2005), 799–815.

• Nonlinear elliptic equations with measures revisited
  In collaboration with Haïm Brezis and Moshe Marcus
  Annals of Math. Studies 163, Princeton University Press, NJ, 2007, pp. 55–110.
  • These results have been announced in a note:
    A new concept of reduced measure for nonlinear elliptic equations
    C. R. Acad. Sci. Paris 339 (2004), 169–174.

• Kato's inequality when \(\Delta u\) is a measure
  In collaboration with Haïm Brezis
  C. R. Acad. Sci. Paris, Ser. I 338 (2004), 599–604.

• \(W^{1, 1}\)-maps with values into \(S^1\)
  In collaboration with Haïm Brezis and Petru Mironescu
  Geometric Analysis of PDE and Several Complex Variables
  (S. Chanillo, P. Cordaro, N. Hanges and A. Meziani, eds.),
  Contemporary Mathematics, 368. American Mathematical Society, Providence, RI, 2005, pp. 69–100.
  Additional results and proofs of some claims are also available (latest version: Dec 30, 2004).

• Singularities of positive supersolutions in elliptic PDEs
  In collaboration with Louis Dupaigne
  Selecta Math. (N.S.) 10 (2004), 341–358.

• A new approach to Sobolev spaces and connections to Γ-convergence
  Calc. Var. Partial Differential Equations 19 (2004), 229–255.
  

• On the distributions of the form \(\sum_i (\delta_{p_i} - \delta_{n_i})\)
  J. Funct. Anal. 210 (2004), 391–435.
  
  • These results have been announced in a note:
    On the distributions of the form \(\sum_i (\delta_{p_i} - \delta_{n_i})\)
    C. R. Acad. Sci. Paris, Ser. I 336 (2003), 571–576.
    

• An estimate in the spirit of Poincarés inequality
  J. Eur. Math. Soc. (JEMS) 6 (2004), 1–15
  
  • These results have been announced in a note:
    A variant of Poincaré's inequality
    C. R. Acad. Sci. Paris, Ser. I 337 (2003), 253–257.

• Remarks on the strong maximum principle
  In collaboration with Haïm Brezis
  Diff. Int. Eq. 16 (2003), 1–12.
  

• Variants of Kato's inequality and removable singularities
  In collaboration with Juan Dávila
  J. Anal. Math. 91 (2003), 143–178.