Augusto Ponce

Detaille, Antoine ; Ponce, Augusto. A decomposition for Borel measures $\mu \leq \mathcal{H}^s$. In: Real Analysis Exchange, Vol. 48, no.1, p. 1-17 (2022). doi:10.14321/realanalexch.48.1.1629953964.

http://hdl.handle.net/2078.1/271635

Buccheri, Stefano ; Orsina, Luigi ; Ponce, Augusto. An Agmon-Allegretto-Piepenbrink principle for Schrödinger operators. In: Real Academia de Ciencias Exactas, Fisicas y Naturales. Revista. Serie A, Matematicas, Vol. 116, no.4, p. 151 (2022). doi:10.1007/s13398-022-01293-7.

http://hdl.handle.net/2078.1/271687

Cufi, Julià ; Ponce, Augusto ; Verdera, Joan. The precise representative for the gradient of the Riesz potential of a finite measure. In: Journal of the London mathematical society, Vol. 106, no. np, p. 1603-1627 (2022). doi:10.1112/jlms.12607.

http://hdl.handle.net/2078.1/271645

Ponce, Augusto ; Wilmet, Nicolas. A representation formula for the distributional normal derivative. In: Revista Matematica Complutense, Vol. 34, no. 3, p. 797–809 (2021). doi:10.1007/s13163-020-00371-x.

http://hdl.handle.net/2078.1/235040

Ponce, Augusto ; Daniel Spector. A Boxing inequality for the fractional perimeter. In: Scuola Normale Superiore di Pisa. Annali. Classe di Scienze, Vol. 20, p. 107–141 (2020). doi:10.2422/2036-2145.201711_012.

http://hdl.handle.net/2078.1/207459

Ponce, Augusto ; Daniel Spector. A decomposition by non-negative functions in the Sobolev space \(W^{k,1}\). In: Indiana University Mathematics Journal, Vol. 69, no. 1, p. 151–169.

http://hdl.handle.net/2078.1/207458

Ambrosio, Luigi ; Ponce, Augusto ; Rodiac, Rémy. Critical weak-$L^p$ differentiability of singular integrals. In: Revista Matematica Iberoamericana, Vol. 36, no. 7, p. 2033–2072 (2020).

http://hdl.handle.net/2078.1/216700

Orsina, Luigi ; Ponce, Augusto. On the nonexistence of Green's function and failure of the strong maximum principle. In: Journal de mathématiques pures et appliquées, Vol. 134, p. 72–121 (2020). doi:10.1016/j.matpur.2019.06.001.

http://hdl.handle.net/2078.1/216690

Ponce, Augusto ; Wilmet, Nicolas. The Hopf lemma for the Schrödinger operator. In: Advanced Nonlinear Studies, Vol. 10, no.2, p. 459–475 (2020). doi:10.1515/ans-2020-2078.

http://hdl.handle.net/2078.1/235057

Ponce, Augusto ; Orsina, Luigi. Hopf potentials for the Schrödinger operator. In: Analysis & PDE, Vol. 11, no.8, p. 2015-2047. doi:10.2140/apde.2018.11.2015.

http://hdl.handle.net/2078.1/200928

Ponce, Augusto ; Wilmet, Nicolas. Optimal Control of Nonlinear Elliptic Problems with Sparsity. In: SIAM Journal on Control and Optimization, Vol. 56, no.4, p. 2513-2535. doi:10.1137/17M1161555.

http://hdl.handle.net/2078.1/200929

Bousquet, Pierre ; Ponce, Augusto ; Van Schaftingen, Jean. Weak approximation by bounded Sobolev maps with values into complete manifolds. In: Comptes Rendus Mathematique, Vol. 356, no. 3, p. 264-271 (2018). doi:10.1016/j.crma.2018.01.017.

http://hdl.handle.net/2078.1/196135

Ponce, Augusto ; Spector, Daniel. A note on the fractional perimeter and interpolation. In: Comptes rendus - Mathématique, Vol. 355, no.9, p. 960-965 (2017). doi:10.1016/j.crma.2017.09.001.

http://hdl.handle.net/2078.1/188484

Bousquet, Pierre ; Ponce, Augusto ; Van Schaftingen, Jean. Density of bounded maps in Sobolev spaces into complete manifolds. In: Annali di Matematica Pura ed Applicata (1923 -), Vol. 196, no. 6, p. 2261–2301 (2017). doi:10.1007/s10231-017-0664-1.

http://hdl.handle.net/2078.1/185227

Orsina, Luigi ; Ponce, Augusto. Flat solutions of the 1-Laplacian equation. In: Universita degli Studi di Trieste. Istituto di Matematica. Rendiconti, Vol. 49, p. 41-51.

http://hdl.handle.net/2078.1/200903

Ponce, Augusto ; Van Schaftingen, Jean. Gauge-measurable functions. In: Universita degli Studi di Trieste. Istituto di Matematica. Rendiconti, Vol. 49, p. 113-135.

http://hdl.handle.net/2078.1/200921

Ponce, Augusto ; Spector, Daniel. On formulae decoupling the total variation of BV functions. In: Nonlinear Analysis: Theory, Methods & Applications, Vol. 154, p. 241-257 (2017). doi:10.1016/j.na.2016.08.028.

http://hdl.handle.net/2078.1/183147

Ponce, Augusto ; Wilmet, Nicolas. Schrödinger operators involving singular potentials and measure data. In: Journal of Differential Equations, Vol. 263, p. 3581-3610 (2017). doi:10.1016/j.jde.2017.04.039.

http://hdl.handle.net/2078.1/185226

Boccardo, Lucio ; Orsina, Luigi ; Ponce, Augusto. The role of interplay between coefficients in the $G$-convergence of some elliptic equations. In: Rendiconti Lincei - Matematica e Applicazioni, Vol. 28, p. 729-745 (2017). doi:10.4171/rlm/783.

http://hdl.handle.net/2078.1/189713

Ponce, Augusto ; Orsina, Luigi. Strong maximum principle for Schrödinger operators with singular potential. In: Annales de l'Institut Henri Poincaré - C - Non Linear Analysis, Vol. 33, no. 2, p. 477-493 (2016). doi:10.1016/j.anihpc.2014.11.004.

http://hdl.handle.net/2078.1/171918

Bousquet, Pierre ; Ponce, Augusto ; Van Schaftingen, Jean. Strong density for higher order Sobolev spaces into compact manifolds. In: Journal of the european mathematical society, Vol. 17, no.4, p. 763-817 (2015). doi:10.4171/JEMS/518.

http://hdl.handle.net/2078.1/158312

Bousquet, Pierre ; Ponce, Augusto ; Van Schaftingen, Jean. Strong approximation of fractional Sobolev maps. In: Journal of Fixed Point Theory and Applications, Vol. 15, no.1, p. 133-153 (2014). doi:10.1007/s11784-014-0172-5.

http://hdl.handle.net/2078.1/153456

Bousquet, Pierre ; Ponce, Augusto ; Van Schaftingen, Jean. Density of smooth maps for fractional Sobolev spaces $W^{s, p}$ into $ell$ simply connected manifolds when $s ge 1$. In: Confluentes Mathematici, Vol. 5, no. 2, p. 3-22 (2013). doi:10.5802/cml.5.

http://hdl.handle.net/2078.1/135962

Ponce, Augusto ; Presoto, Adilson E.. Limit solutions of the Chern–Simons equation. In: Nonlinear Analysis: Theory, Methods & Applications, Vol. 84, p. 91-102 (2013). doi:10.1016/j.na.2013.02.004.

http://hdl.handle.net/2078.1/130265

Ponce, Augusto. Singularities of the divergence of continuous vector fields and uniform Hausdorff estimates. In: Indiana University Mathematics Journal, Vol. 62, no. 4, p. 1055-1074 (2013). doi:10.1512/iumj.2013.62.5079.

http://hdl.handle.net/2078.1/115695

Ponce, Augusto ; Porretta, Alessio ; Petitta, Francesco. Diffuse measures and nonlinear parabolic equations. In: Journal of Evolution Equations, Vol. 11, no. 1, p. 861–905 (2011). doi:10.1007/s00028-011-0115-1.

http://hdl.handle.net/2078.1/105502

Ponce, Augusto ; Véron, Laurent ; Bidaut-Véron, Marie-Françoise. Isolated boundary singularities of semilinear elliptic equations. In: Calculus of Variations and Partial Differential Equations, Vol. 40, no. 1-2, p. 183-221 (2011). doi:10.1007/s00526-010-0337-z.

http://hdl.handle.net/2078.1/105497

Marcus, Moshe ; Ponce, Augusto. Reduced limits for nonlinear equations with measures. In: Journal of Functional Analysis, Vol. 258, no. 7, p. 2316-2372 (2010). doi:10.1016/j.jfa.2009.09.007.

http://hdl.handle.net/2078.1/34185

Ponce, Augusto ; Van Schaftingen, Jean. Closure of smooth maps in W^{1,p}(B^3; S^2). In: Differential and Integral Equations : an international journal for theory & applications, Vol. 22, no. 9-10, p. 881-900 (2009).

http://hdl.handle.net/2078.1/58605

Bousquet, Pierre ; Ponce, Augusto ; Van Schaftingen, Jean. A case of density in W^{2,p}(M; N). In: Comptes rendus - Mathématique, Vol. 346, no. 13-14, p. 735-740 (2008). doi:10.1016/j.crma.2008.05.006.

http://hdl.handle.net/2078.1/36411

Petitta, Francesco ; Porretta, Alessio ; Ponce, Augusto. Approximation of diffuse measures for parabolic capacities. In: Comptes rendus - Mathématique, Vol. 346, no. 3-4, p. 161-166 (2008). doi:10.1016/j.crma.2007.12.002.

http://hdl.handle.net/2078.1/70511

Davila, Juan ; Ponce, Augusto. Hausdorff dimension of rupture sets and removable singularities. In: Comptes rendus - Mathématique, Vol. 346, no. 1-2, p. 27-32 (2008). doi:10.1016/j.crma.2007.11.007.

http://hdl.handle.net/2078.1/70509

Brezis, Haïm ; Ponce, Augusto. Kato's Inequality Up To the Boundary. In: Communications in Contemporary Mathematics, Vol. 10, no. 6, p. 1217-1241 (2008). doi:10.1142/S0219199708003241.

http://hdl.handle.net/2078.1/35893

Orsina, Luigi ; Ponce, Augusto. Semilinear elliptic equations and systems with diffuse measures. In: Journal of Evolution Equations, Vol. 8, no. 4, p. 781-812 (2008). doi:10.1007/s00028-008-0446-32.

http://hdl.handle.net/2078.1/35823

Montenegro, Marcelo ; Ponce, Augusto. The sub-supersolution method for weak solutions. In: Proceedings of the American Mathematical Society, Vol. 136, no. 7, p. 2429-2438 (2008). doi:10.1090/S0002-9939-08-09231-9.

http://hdl.handle.net/2078.1/70512

Lin, Chang-Shou ; Yang, Yisong ; Ponce, Augusto. A system of elliptic equations arising in Chern-Simons field theory. In: Journal of functional analysis, Vol. 247, no. 2, p. 289-350 (2007). doi:10.1016/j.jfa.2007.03.010.

http://hdl.handle.net/2078.1/70497

Bidaut-Véron, Marie-Françoise ; Véron, Laurent ; Ponce, Augusto. Boundary singularities of positive solutions of some nonlinear elliptic equations. In: Comptes rendus - Mathématique, Vol. 344, no. 2, p. 83-88 (2007). doi:10.1016/j.crma.2006.11.027.

http://hdl.handle.net/2078.1/70518

Ponce, Augusto ; Van Schaftingen, Jean. The continuity of functions with N-th derivative measure. In: Houston Journal of Mathematics, Vol. 33, no. 3, p. 927-939 (2007).

http://hdl.handle.net/2078.1/36944

Dupaigne, Louis ; Porretta, Alessio ; Ponce, Augusto. Elliptic equations with vertical asymptotes in the nonlinear term. In: Journal d'Analyse Mathematique, Vol. 98, no. 1, p. 349-396 (2006). doi:10.1007/BF02790280.

http://hdl.handle.net/2078.1/70508

Brezis, Haim ; Ponce, Augusto. Reduced measures for obstacle problems. In: Advances in Differential Equations, Vol. 10, no. 11, p. 1201-1234 (2005).

http://hdl.handle.net/2078.1/70519

Brezis, Haïm ; Ponce, Augusto. Reduced measures on the boundary. In: International Journal of Functional Analysis, Operator Theory & Applications, Vol. 229, no. 1, p. 95-120 (2005). doi:10.1016/j.jfa.2004.12.001.

http://hdl.handle.net/2078.1/70506

Bartolucci, Daniele ; Leoni, Fabiana ; Orsina, Luigi ; Ponce, Augusto. Semilinear equations with exponential nonlinearity and measure data. In: Annales de l'Institut Henri Poincare (C) Non Linear Analysis, Vol. 22, no. 6, p. 799-815 (2005). doi:10.1016/j.anihpc.2004.12.003.

http://hdl.handle.net/2078.1/70475

Ponce, Augusto. A new approach to Sobolev spaces and connections to Gamma-convergence . In: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, Vol. 19, no. 3, p. 229-255 (2004). doi:10.1007/s00526-003-0195-z.

http://hdl.handle.net/2078.1/70500

Brezis, Haim ; Marcus, Moshe ; Ponce, Augusto. A new concept of reduced measure for nonlinear elliptic equations. In: COMPTES RENDUS MATHEMATIQUE, Vol. 339, no. 3, p. 169-174 (2004). doi:10.1016/j.crma.2004.05.012.

http://hdl.handle.net/2078.1/70504

Ponce, Augusto. An estimate in the spirit of Poincaré's inequality . In: JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, Vol. 6, no. 1, p. 1-15 (2004).

http://hdl.handle.net/2078.1/70463

Brezis, Haim ; Ponce, Augusto. Kato's inequality when Delta u is a measure. In: COMPTES RENDUS MATHEMATIQUE, Vol. 338, no. 8, p. 599-604 (2004). doi:10.1016/j.crma.2003.12.032.

http://hdl.handle.net/2078.1/70476

Ponce, Augusto. On the distributions of the form Sum_i (delta_{p_i} - delta_{n_i}). In: JOURNAL OF FUNCTIONAL ANALYSIS, Vol. 210, no. 2, p. 391-435 (2004). doi:10.1016/S0022-1236(03)00239-8.

http://hdl.handle.net/2078.1/70414

Dupaigne, Louis ; Ponce, Augusto. Singularities of positive supersolutions in elliptic PDEs. In: Selecta Math. (N.S.), Vol. 10, no. 3, p. 341-358 (2004). doi:10.1007/s00029-004-0390-6.

http://hdl.handle.net/2078.1/70520

Ponce, Augusto. A variant of Poincaré's inequality . In: COMPTES RENDUS MATHEMATIQUE, Vol. 337, no. 4, p. 253-257 (2003). doi:10.1016/S1631-073X(03)00313-3.

http://hdl.handle.net/2078.1/70426

Ponce, Augusto. On the distributions of the form Sum_i (delta_{p_i} - delta_{n_i}) . In: COMPTES RENDUS MATHEMATIQUE, Vol. 336, no. 7, p. 571-576 (2003). doi:10.1016/S1631-073X(03)00133-X.

http://hdl.handle.net/2078.1/70411

Brezis, Haim ; Ponce, Augusto. Remarks on the strong maximum principle. In: Diff. Int. Eq., Vol. 16, no. 1, p. 1-12 (2003).

http://hdl.handle.net/2078.1/70513

Davila, Juan ; Ponce, Augusto. Variants of Kato's inequality and removable singularities. In: JOURNAL D ANALYSE MATHEMATIQUE, Vol. 91, no. 1, p. 143-178 (2003). doi:10.1007/BF02788785.

http://hdl.handle.net/2078.1/70502

Ponce, Augusto. Elliptic PDEs, Measures and Capacities. From the Poisson equation to nonlinear Thomas-Fermi problems, 1st edition (EMS Tracts in Mathematics; 23), EMS Publishing House: Zürich, 2016. 978-3-03719-140-8. 460 p.

http://hdl.handle.net/2078.1/171919

Ponce, Augusto. Métodos Clássicos em Teoria do Potencial [Méthodes Classiques en Théorie du Potentiel], 1re édition (Publicações matemáticas; 24), IMPA: Rio de Janeiro, 2009. 978-85-244-0244-9. 170 p.

http://hdl.handle.net/2078.1/70517

Brezis, Haim ; Marcus, Moshe ; Ponce, Augusto. Nonlinear elliptic equations with measures revisited. In: J. Bourgain, C. Kenig, S. Klainerman, Mathematical Aspects of Nonlinear Dispersive Equations, Princeton University Press: Princeton, NJ, 2007, p. 55-110. 978-0-691-12955-6.

http://hdl.handle.net/2078.1/70516

Ponce, Augusto. How to construct good measures. In: C. Bandle, H. Berestycki, B. Brighi, A. Brillard, M. Chipot, J.-M. Coron, C. Sbordone, I. Shafrir, V. Valente et G. Vergara-Caffarelli, Elliptic and parabolic problems, Birkhäuser: Verlag Basel, 2005, p. 335-348. 978-3-7643-7249-1.

http://hdl.handle.net/2078.1/70515

Brezis, Haim ; Mironescu, Petru ; Ponce, Augusto. W^{1,1}-maps with values into S^1. In: S. Chanillo, P. Cordaro, N. Hanges et A. Meziani, Geometric Analysis of PDE and Several Complex Variables, Amer. Math. Soc.: Providence, RI, 2005, p. 69-100. 0-8218-3386-3.

http://hdl.handle.net/2078.1/70514