Geodesic
Finite Energy Solutions of Nonlinear Dirichlet Problems with Discontinuous Coefficients
Bollettino della Unione matematica italiana, Série 9, Tome 5 (2012) no. 2, pp. 357-368.

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

This paper dedicated to the memory of Enrico Magenes, concerning a nonlinear Dirichlet problem, follows the previous one ([1]) dedicated to the memory of Guido Stampacchia, concerning a similar linear problem (see [14]). 
@article{BUMI_2012_9_5_2_a9,
     author = {Boccardo, Lucio},
     title = {Finite {Energy} {Solutions} of {Nonlinear} {Dirichlet} {Problems} with {Discontinuous} {Coefficients}},
     journal = {Bollettino della Unione matematica italiana},
     pages = {357--368},
     publisher = {mathdoc},
     volume = {Ser. 9, 5},
     number = {2},
     year = {2012},
     zbl = {1258.35095},
     mrnumber = {2977253},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BUMI_2012_9_5_2_a9/}
}
TY  - JOUR
AU  - Boccardo, Lucio
TI  - Finite Energy Solutions of Nonlinear Dirichlet Problems with Discontinuous Coefficients
JO  - Bollettino della Unione matematica italiana
PY  - 2012
SP  - 357
EP  - 368
VL  - 5
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/BUMI_2012_9_5_2_a9/
LA  - en
ID  - BUMI_2012_9_5_2_a9
ER  - 
%0 Journal Article
%A Boccardo, Lucio
%T Finite Energy Solutions of Nonlinear Dirichlet Problems with Discontinuous Coefficients
%J Bollettino della Unione matematica italiana
%D 2012
%P 357-368
%V 5
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/BUMI_2012_9_5_2_a9/
%G en
%F BUMI_2012_9_5_2_a9
Boccardo, Lucio. Finite Energy Solutions of Nonlinear Dirichlet Problems with Discontinuous Coefficients. Bollettino della Unione matematica italiana, Série 9, Tome 5 (2012) no. 2, pp. 357-368. http://geodesic.mathdoc.fr/item/BUMI_2012_9_5_2_a9/

[1] L. Boccardo, Some developments on Dirichlet problems with discontinuous coefficients, Boll. Unione Mat. Ital., 2 (2009), 285-297. | fulltext bdim | fulltext EuDML | MR | Zbl

[2] L. Boccardo, A remark on some nonlinear elliptic problems, 2001-Luminy Conference on Quasilinear Elliptic and Parabolic Equations and Systems, Electron. J. Diff. Eqns., Conf., 8 (2002), 47-52. | fulltext EuDML | MR | Zbl

[3] L. Boccardo - A. Dall'Aglio - L. Orsina, Existence and regularity results for some elliptic equations with degenerate coercivity. Dedicated to Prof. C. Vinti (Italian) (Perugia, 1996). Atti Sem. Mat. Fis. Univ. Modena, 46 (1998), suppl., 51-81. | MR

[4] L. Boccardo - D. Giachetti, Existence results via regularity for some nonlinear elliptic problems, Comm. P.D.E., 14 (1989), 663-680. | DOI | MR | Zbl

[5] L. Boccardo - D. Giachetti, A nonlinear interpolation result with application to the summability of minima of some integral functionals, Discrete and Continuous Dynamical Systems, Series B, 11 (2009), 31-42. | DOI | MR | Zbl

[6] L. Boccardo - J. I. Diaz - D. Giachetti - F. Murat, Existence and regularity of renormalized solutions for some elliptic problems involving derivatives of nonlinear terms, J. Diff. Eq., 106 (1993), 215-237. | DOI | MR | Zbl

[7] L. Boccardo - T. Gallouet - F. Murat, Unicité de la solution pour des equations elliptiques non linéaires, C. R. Acad. Sc. Paris, 315 (1992), 1159-1164. | MR

[8] L. Boccardo - F. Murat, Almost everywhere convergence of the gradients of solutions to elliptic and parabolic equations, Nonlinear Anal TMA, 19 (1992), 581- 597. | DOI | MR | Zbl

[9] L. Boccardo - F. Murat - J.-P. Puel, Existence of bounded solutions for nonlinear elliptic unilateral problems, Ann. Mat. Pura Appl., 152 (1988), 183-196. | DOI | MR | Zbl

[10] H. Brezis, Equations et inéquations non linéaires dans les espaces vectoriels en dualité, Ann. Inst. Fourier (Grenoble), 18 (1968), 115-175. | fulltext EuDML | MR | Zbl

[11] F. E. Browder, Existence theorems for nonlinear partial differential equations, Proceedings of Symposia in Pure Mathematics, vol. XVI, American Mathematical Society, Providence (1970), 1-60. | MR

[12] J. Casado-Diaz - F. Murat - A. Porretta, Uniqueness results for pseudomonotone problems with $p > 2$, C. R. Math. Acad. Sci. Paris, 344 (2007), 487-492. | DOI | MR | Zbl

[13] J. Leray - J. L. Lions, Quelques résultats de Višik sur les problèmes elliptiques semi-linéaires par les méthodes de Minty et Browder, Bull. Soc. Math. France, 93 (1965), 97-107. | fulltext EuDML | MR | Zbl

[14] E. Magenes - G. Stampacchia, I problemi al contorno per le equazioni differenziali di tipo ellittico, Ann. Scuola Norm. Sup. Pisa, 12 (1958), 247-358. | fulltext EuDML | MR

[15] G. Moscariello, Existence and uniquesness for elliptic equations with lower-order terms, Adv. Calc. Var., 4 (2011), 421-444. | DOI | MR | Zbl

[16] S. Puglisi, Some regularity results for solutions to Dirichlet problems with discontinuous coefficients, preprint. | Zbl

[17] G. Stampacchia, Le probléme de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus, Ann. Inst. Fourier (Grenoble), 15 (1965), 189-258. | fulltext EuDML | MR | Zbl

[18] G. Zecca, Existence and uniqueness for nonlinear elliptic equations with lower-order terms, Nonlinear Anal., 75 (2012), 899-912. | DOI | MR | Zbl