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M. Augusto Ponce

SST/SC - Faculté des sciences
SST/SC/MATH - Ecole de mathématique (MATH)
SST/IRMP - Institut de recherche en mathématique et physique (IRMP)

Address
  MATH - Chemin du Cyclotron 2 bte L7.01.02 à 1348 Louvain-la-Neuve
E-mail
 
MATH
  Phone : 010 47 86 74
  Building : Marc De Hemptinne; Floor 01; Office B 127; Site Louvain-la-Neuve




Degrees

year

degree title

institution

1998Licence en mathématiquesUnicamp
1999Baccalauréat en mathématiquesUniversidade Estadual de Campinas
2000Master en mathématiquesUnicamp
2000Master en mathématiquesUniversidade Estadual de Campinas
2004Docteur en mathématiques appliquéesUniversité Pierre et Marie Curie : Paris VI
2005PhD en mathématiquesRutgers University


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    2011

    Article de périodique (Journal article)


  • Bidaut-Véron, Marie-Françoise; Véron, Laurent; Ponce, Augusto (2011). Isolated boundary singularities of semilinear elliptic equations. In : CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS (2011), p. 183-221. doi: 10.1007/s00526-010-0337-z. http://hdl.handle.net/2078.1/70482.

  • Ponce, Augusto; Porretta, Alessio; Petitta, Francesco (2011). Diffuse measures and nonlinear parabolic equations. In : Journal of Evolution Equations (2011), p. 861–905. doi: 10.1007/s00028-011-0115-1. http://hdl.handle.net/2078.1/105502.

  • Ponce, Augusto; Véron, Laurent; Bidaut-Véron, Marie-Françoise (2011). Isolated boundary singularities of semilinear elliptic equations. In : Calculus of Variations and Partial Differential Equations (2011), p. 183-221. doi: 10.1007/s00526-010-0337-z. http://hdl.handle.net/2078.1/105497.

    • 2010

    Article de périodique (Journal article)


  • Marcus, Moshe; Ponce, Augusto (2010). Reduced limits for nonlinear equations with measures. In : Journal of Functional Analysis (2010), p. 2316-2372. doi: 10.1016/j.jfa.2009.09.007. http://hdl.handle.net/2078.1/34185.

    • 2009

    Communication à un colloque (Conference Paper)


  • Ponce, Augusto; Van Schaftingen, Jean (2009). Closure of smooth maps in W^{1,p}(B^3; S^2). In : Differential and Integral Equations : an international journal for theory & applications (2009), p. 881-900. Conference on Nonlinear Differential Equations, Acad Royale Belgique, Brussels (Belgium) Sep 10-12, 2008. http://hdl.handle.net/2078.1/58605.

    • 2008

    Article de périodique (Journal article)


  • Montenegro, Marcelo; Ponce, Augusto (2008). The sub-supersolution method for weak solutions. In : PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY (2008), p. 2429-2438. doi: 10.1090/S0002-9939-08-09231-9. http://hdl.handle.net/2078.1/70512.

  • Davila, Juan; Ponce, Augusto (2008). Hausdorff dimension of rupture sets and removable singularities. In : COMPTES RENDUS MATHEMATIQUE (2008), p. 27-32. doi: 10.1016/j.crma.2007.11.007. http://hdl.handle.net/2078.1/70509.

  • Petitta, Francesco; Porretta, Alessio; Ponce, Augusto (2008). Approximation of diffuse measures for parabolic capacities. In : COMPTES RENDUS MATHEMATIQUE (2008), p. 161-166. doi: 10.1016/j.crma.2007.12.002. http://hdl.handle.net/2078.1/70511.

  • Brezis, Haïm; Ponce, Augusto (2008). Kato's Inequality Up To the Boundary. In : Communications in Contemporary Mathematics (2008), p. 1217-1241. doi: 10.1142/S0219199708003241. http://hdl.handle.net/2078.1/35893.

  • Orsina, Luigi; Ponce, Augusto (2008). Semilinear elliptic equations and systems with diffuse measures. In : Journal of Evolution Equations (2008), p. 781-812. doi: 10.1007/s00028-008-0446-32. http://hdl.handle.net/2078.1/35823.

  • Bousquet, Pierre; Ponce, Augusto; Van Schaftingen, Jean (2008). A case of density in W^{2,p}(M; N). In : Comptes rendus - Mathématique (2008), p. 735-740. doi: 10.1016/j.crma.2008.05.006. http://hdl.handle.net/2078.1/36411.

    • 2007

    Article de périodique (Journal article)


  • Lin, Chang-Shou; Yang, Yisong; Ponce, Augusto (2007). A system of elliptic equations arising in Chern-Simons field theory. In : JOURNAL OF FUNCTIONAL ANALYSIS (2007), p. 289-350. doi: 10.1016/j.jfa.2007.03.010. http://hdl.handle.net/2078.1/70497.

  • Bidaut-Véron, Marie-Françoise; Véron, Laurent; Ponce, Augusto (2007). Boundary singularities of positive solutions of some nonlinear elliptic equations. In : C. R. Acad. Sci. Paris (2007), p. 83-88. doi: 10.1016/j.crma.2006.11.027. http://hdl.handle.net/2078.1/70518.

  • Ponce, Augusto; Van Schaftingen, Jean (2007). The continuity of functions with N-th derivative measure. In : Houston Journal of Mathematics (2007), p. 927-939. http://hdl.handle.net/2078.1/36944.

    • Contribution à ouvrage collectif (Book Chapter)


  • Brezis, Haim; Marcus, Moshe; Ponce, Augusto (2007). Nonlinear elliptic equations with measures revisited. In :J. Bourgain, C. Kenig, S. Klainerman, Mathematical Aspects of Nonlinear Dispersive Equations, Princeton, NJ : Princeton University Press, p. 55-110. http://hdl.handle.net/2078.1/70516.

    • 2006

    Article de périodique (Journal article)


  • Dupaigne, Louis; Porretta, Alessio; Ponce, Augusto (2006). Elliptic equations with vertical asymptotes in the nonlinear term. In : JOURNAL D ANALYSE MATHEMATIQUE (2006), p. 349-396. doi: 10.1007/BF02790280. http://hdl.handle.net/2078.1/70508.

    • Monographie (Book)


  • Ponce, Augusto (2006). Métodos Clássicos em Teoria do Potencial [Méthodes Classiques en Théorie du Potentiel]. IMPA : Rio de Janeiro. p. 170. http://hdl.handle.net/2078.1/70517.

    • 2005

    Article de périodique (Journal article)


  • Brezis, Haïm; Ponce, Augusto (2005). Reduced measures on the boundary. In : JOURNAL OF FUNCTIONAL ANALYSIS (2005), p. 95-120. doi: 10.1016/j.jfa.2004.12.001. http://hdl.handle.net/2078.1/70506.

  • Brezis, Haim; Ponce, Augusto (2005). Reduced measures for obstacle problems. In : Adv. Diff. Eq. (2005), p. 1201-1234. http://hdl.handle.net/2078.1/70519.

  • Bartolucci, Daniele; Leoni, Fabiana; Orsina, Luigi; Ponce, Augusto (2005). Semilinear equations with exponential nonlinearity and measure data. In : Annales de l'Institut Henri Poincare (C) Non Linear Analysis (2005), p. 799-815. doi: 10.1016/j.anihpc.2004.12.003. http://hdl.handle.net/2078.1/70475.

    • Contribution à ouvrage collectif (Book Chapter)


  • Ponce, Augusto (2005). 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, Verlag Basel : Birkhäuser, p. 335-348. http://hdl.handle.net/2078.1/70515.

    • 2004

    Article de périodique (Journal article)


  • Ponce, Augusto (2004). A new approach to Sobolev spaces and connections to Gamma-convergence. In : CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS (2004), p. 229-255. doi: 10.1007/s00526-003-0195-z. http://hdl.handle.net/2078.1/70500.

  • Brezis, Haim; Marcus, Moshe; Ponce, Augusto (2004). A new concept of reduced measure for nonlinear elliptic equations. In : COMPTES RENDUS MATHEMATIQUE (2004), p. 169-174. doi: 10.1016/j.crma.2004.05.012. http://hdl.handle.net/2078.1/70504.

  • Dupaigne, Louis; Ponce, Augusto (2004). Singularities of positive supersolutions in elliptic PDEs. In : Selecta Math. (N.S.) (2004), p. 341-358. doi: 10.1007/s00029-004-0390-6. http://hdl.handle.net/2078.1/70520.

  • Ponce, AC; Ponce, Augusto (2004). On the distributions of the form Sum_i (delta_{p_i} - delta_{n_i}). In : JOURNAL OF FUNCTIONAL ANALYSIS (2004), p. 391-435. doi: 10.1016/S0022-1236(03)00239-8. http://hdl.handle.net/2078.1/70414.

  • Ponce, Augusto (2004). An estimate in the spirit of Poincaré's inequality. In : JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY (2004), p. 1-15. http://hdl.handle.net/2078.1/70463.

  • Brezis, Haim; Ponce, Augusto (2004). Kato's inequality when Delta u is a measure. In : COMPTES RENDUS MATHEMATIQUE (2004), p. 599-604. doi: 10.1016/j.crma.2003.12.032. http://hdl.handle.net/2078.1/70476.

    • Contribution à ouvrage collectif (Book Chapter)


  • Brezis, Haim; Mironescu, Petru; Ponce, Augusto (2004). 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, Providence, RI : Amer. Math. Soc., p. 69-100. http://hdl.handle.net/2078.1/70514.

    • 2003

    Article de périodique (Journal article)


  • Davila, Juan; Ponce, Augusto (2003). Variants of Kato's inequality and removable singularities. In : JOURNAL D ANALYSE MATHEMATIQUE (2003), p. 143-178. doi: 10.1007/BF02788785. http://hdl.handle.net/2078.1/70502.

  • Ponce, Augusto (2003). On the distributions of the form Sum_i (delta_{p_i} - delta_{n_i}). In : COMPTES RENDUS MATHEMATIQUE (2003), p. 571-576. doi: 10.1016/S1631-073X(03)00133-X. http://hdl.handle.net/2078.1/70411.

  • Ponce, Augusto (2003). A variant of Poincaré's inequality. In : COMPTES RENDUS MATHEMATIQUE (2003), p. 253-257. doi: 10.1016/S1631-073X(03)00313-3. http://hdl.handle.net/2078.1/70426.

  • Brezis, Haim; Ponce, Augusto (2003). Remarks on the strong maximum principle. In : Diff. Int. Eq. (2003), p. 1-12. http://hdl.handle.net/2078.1/70513.

Biography

Degrees

year

degree title

institution

1998Licence en mathématiquesUnicamp
1999Baccalauréat en mathématiquesUniversidade Estadual de Campinas
2000Master en mathématiquesUnicamp
2000Master en mathématiquesUniversidade Estadual de Campinas
2004Docteur en mathématiques appliquéesUniversité Pierre et Marie Curie : Paris VI
2005PhD en mathématiquesRutgers University


Teaching

Courses

Academic Year 2011 - 2012
LMAT 1111 A General Mathematics
LMAT 1111 B General Mathematics
LMAT 1111 C General Mathematics
LMAT 1111 D General Mathematics
LMAT 1111 E General Mathematics
LMAT 1111 F General Mathematics
LMAT 1111 G General Mathematics
LMAT 1111 General Mathematics
LMAT 1121 Mathematical analysis 1
LMAT 1122 Mathematical analysis 2
LMAT 1221 Mathematical analysis 3
LMAT 1381 Personal project and seminary
LMAT 2130 Partial differential equations : Poisson and Laplace equations
LMAT 2410 Partial differential equation : heat equation, brownian moves and numerical aspects


Publications

| |

    2011

    Article de périodique (Journal article)


  • Bidaut-Véron, Marie-Françoise; Véron, Laurent; Ponce, Augusto (2011). Isolated boundary singularities of semilinear elliptic equations. In : CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS (2011), p. 183-221. doi: 10.1007/s00526-010-0337-z. http://hdl.handle.net/2078.1/70482.

  • Ponce, Augusto; Porretta, Alessio; Petitta, Francesco (2011). Diffuse measures and nonlinear parabolic equations. In : Journal of Evolution Equations (2011), p. 861–905. doi: 10.1007/s00028-011-0115-1. http://hdl.handle.net/2078.1/105502.

  • Ponce, Augusto; Véron, Laurent; Bidaut-Véron, Marie-Françoise (2011). Isolated boundary singularities of semilinear elliptic equations. In : Calculus of Variations and Partial Differential Equations (2011), p. 183-221. doi: 10.1007/s00526-010-0337-z. http://hdl.handle.net/2078.1/105497.

    • 2010

    Article de périodique (Journal article)


  • Marcus, Moshe; Ponce, Augusto (2010). Reduced limits for nonlinear equations with measures. In : Journal of Functional Analysis (2010), p. 2316-2372. doi: 10.1016/j.jfa.2009.09.007. http://hdl.handle.net/2078.1/34185.

    • 2009

    Communication à un colloque (Conference Paper)


  • Ponce, Augusto; Van Schaftingen, Jean (2009). Closure of smooth maps in W^{1,p}(B^3; S^2). In : Differential and Integral Equations : an international journal for theory & applications (2009), p. 881-900. Conference on Nonlinear Differential Equations, Acad Royale Belgique, Brussels (Belgium) Sep 10-12, 2008. http://hdl.handle.net/2078.1/58605.

    • 2008

    Article de périodique (Journal article)


  • Montenegro, Marcelo; Ponce, Augusto (2008). The sub-supersolution method for weak solutions. In : PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY (2008), p. 2429-2438. doi: 10.1090/S0002-9939-08-09231-9. http://hdl.handle.net/2078.1/70512.

  • Davila, Juan; Ponce, Augusto (2008). Hausdorff dimension of rupture sets and removable singularities. In : COMPTES RENDUS MATHEMATIQUE (2008), p. 27-32. doi: 10.1016/j.crma.2007.11.007. http://hdl.handle.net/2078.1/70509.

  • Petitta, Francesco; Porretta, Alessio; Ponce, Augusto (2008). Approximation of diffuse measures for parabolic capacities. In : COMPTES RENDUS MATHEMATIQUE (2008), p. 161-166. doi: 10.1016/j.crma.2007.12.002. http://hdl.handle.net/2078.1/70511.

  • Brezis, Haïm; Ponce, Augusto (2008). Kato's Inequality Up To the Boundary. In : Communications in Contemporary Mathematics (2008), p. 1217-1241. doi: 10.1142/S0219199708003241. http://hdl.handle.net/2078.1/35893.

  • Orsina, Luigi; Ponce, Augusto (2008). Semilinear elliptic equations and systems with diffuse measures. In : Journal of Evolution Equations (2008), p. 781-812. doi: 10.1007/s00028-008-0446-32. http://hdl.handle.net/2078.1/35823.

  • Bousquet, Pierre; Ponce, Augusto; Van Schaftingen, Jean (2008). A case of density in W^{2,p}(M; N). In : Comptes rendus - Mathématique (2008), p. 735-740. doi: 10.1016/j.crma.2008.05.006. http://hdl.handle.net/2078.1/36411.

    • 2007

    Article de périodique (Journal article)


  • Lin, Chang-Shou; Yang, Yisong; Ponce, Augusto (2007). A system of elliptic equations arising in Chern-Simons field theory. In : JOURNAL OF FUNCTIONAL ANALYSIS (2007), p. 289-350. doi: 10.1016/j.jfa.2007.03.010. http://hdl.handle.net/2078.1/70497.

  • Bidaut-Véron, Marie-Françoise; Véron, Laurent; Ponce, Augusto (2007). Boundary singularities of positive solutions of some nonlinear elliptic equations. In : C. R. Acad. Sci. Paris (2007), p. 83-88. doi: 10.1016/j.crma.2006.11.027. http://hdl.handle.net/2078.1/70518.

  • Ponce, Augusto; Van Schaftingen, Jean (2007). The continuity of functions with N-th derivative measure. In : Houston Journal of Mathematics (2007), p. 927-939. http://hdl.handle.net/2078.1/36944.

    • Contribution à ouvrage collectif (Book Chapter)


  • Brezis, Haim; Marcus, Moshe; Ponce, Augusto (2007). Nonlinear elliptic equations with measures revisited. In :J. Bourgain, C. Kenig, S. Klainerman, Mathematical Aspects of Nonlinear Dispersive Equations, Princeton, NJ : Princeton University Press, p. 55-110. http://hdl.handle.net/2078.1/70516.

    • 2006

    Article de périodique (Journal article)


  • Dupaigne, Louis; Porretta, Alessio; Ponce, Augusto (2006). Elliptic equations with vertical asymptotes in the nonlinear term. In : JOURNAL D ANALYSE MATHEMATIQUE (2006), p. 349-396. doi: 10.1007/BF02790280. http://hdl.handle.net/2078.1/70508.

    • Monographie (Book)


  • Ponce, Augusto (2006). Métodos Clássicos em Teoria do Potencial [Méthodes Classiques en Théorie du Potentiel]. IMPA : Rio de Janeiro. p. 170. http://hdl.handle.net/2078.1/70517.

    • 2005

    Article de périodique (Journal article)


  • Brezis, Haïm; Ponce, Augusto (2005). Reduced measures on the boundary. In : JOURNAL OF FUNCTIONAL ANALYSIS (2005), p. 95-120. doi: 10.1016/j.jfa.2004.12.001. http://hdl.handle.net/2078.1/70506.

  • Brezis, Haim; Ponce, Augusto (2005). Reduced measures for obstacle problems. In : Adv. Diff. Eq. (2005), p. 1201-1234. http://hdl.handle.net/2078.1/70519.

  • Bartolucci, Daniele; Leoni, Fabiana; Orsina, Luigi; Ponce, Augusto (2005). Semilinear equations with exponential nonlinearity and measure data. In : Annales de l'Institut Henri Poincare (C) Non Linear Analysis (2005), p. 799-815. doi: 10.1016/j.anihpc.2004.12.003. http://hdl.handle.net/2078.1/70475.

    • Contribution à ouvrage collectif (Book Chapter)


  • Ponce, Augusto (2005). 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, Verlag Basel : Birkhäuser, p. 335-348. http://hdl.handle.net/2078.1/70515.

    • 2004

    Article de périodique (Journal article)


  • Ponce, Augusto (2004). A new approach to Sobolev spaces and connections to Gamma-convergence. In : CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS (2004), p. 229-255. doi: 10.1007/s00526-003-0195-z. http://hdl.handle.net/2078.1/70500.

  • Brezis, Haim; Marcus, Moshe; Ponce, Augusto (2004). A new concept of reduced measure for nonlinear elliptic equations. In : COMPTES RENDUS MATHEMATIQUE (2004), p. 169-174. doi: 10.1016/j.crma.2004.05.012. http://hdl.handle.net/2078.1/70504.

  • Dupaigne, Louis; Ponce, Augusto (2004). Singularities of positive supersolutions in elliptic PDEs. In : Selecta Math. (N.S.) (2004), p. 341-358. doi: 10.1007/s00029-004-0390-6. http://hdl.handle.net/2078.1/70520.

  • Ponce, AC; Ponce, Augusto (2004). On the distributions of the form Sum_i (delta_{p_i} - delta_{n_i}). In : JOURNAL OF FUNCTIONAL ANALYSIS (2004), p. 391-435. doi: 10.1016/S0022-1236(03)00239-8. http://hdl.handle.net/2078.1/70414.

  • Ponce, Augusto (2004). An estimate in the spirit of Poincaré's inequality. In : JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY (2004), p. 1-15. http://hdl.handle.net/2078.1/70463.

  • Brezis, Haim; Ponce, Augusto (2004). Kato's inequality when Delta u is a measure. In : COMPTES RENDUS MATHEMATIQUE (2004), p. 599-604. doi: 10.1016/j.crma.2003.12.032. http://hdl.handle.net/2078.1/70476.

    • Contribution à ouvrage collectif (Book Chapter)


  • Brezis, Haim; Mironescu, Petru; Ponce, Augusto (2004). 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, Providence, RI : Amer. Math. Soc., p. 69-100. http://hdl.handle.net/2078.1/70514.

    • 2003

    Article de périodique (Journal article)


  • Davila, Juan; Ponce, Augusto (2003). Variants of Kato's inequality and removable singularities. In : JOURNAL D ANALYSE MATHEMATIQUE (2003), p. 143-178. doi: 10.1007/BF02788785. http://hdl.handle.net/2078.1/70502.

  • Ponce, Augusto (2003). On the distributions of the form Sum_i (delta_{p_i} - delta_{n_i}). In : COMPTES RENDUS MATHEMATIQUE (2003), p. 571-576. doi: 10.1016/S1631-073X(03)00133-X. http://hdl.handle.net/2078.1/70411.

  • Ponce, Augusto (2003). A variant of Poincaré's inequality. In : COMPTES RENDUS MATHEMATIQUE (2003), p. 253-257. doi: 10.1016/S1631-073X(03)00313-3. http://hdl.handle.net/2078.1/70426.

  • Brezis, Haim; Ponce, Augusto (2003). Remarks on the strong maximum principle. In : Diff. Int. Eq. (2003), p. 1-12. http://hdl.handle.net/2078.1/70513.


| 2/07/2009 |