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_357_0, author = {Lucio Boccardo}, title = {Finite Energy Solutions of Nonlinear Dirichlet Problems with Discontinuous Coefficients}, journal = {Bollettino dell'Unione Matematica Italiana}, volume = {5}, year = {2012}, pages = {357-368}, zbl = {1258.35095}, mrnumber = {2977253}, language = {en}, url = {http://dml.mathdoc.fr/item/BUMI_2012_9_5_2_357_0} }
Boccardo, Lucio. Finite Energy Solutions of Nonlinear Dirichlet Problems with Discontinuous Coefficients. Bollettino dell'Unione Matematica Italiana, Tome 5 (2012) pp. 357-368. http://gdmltest.u-ga.fr/item/BUMI_2012_9_5_2_357_0/
[1] Some developments on Dirichlet problems with discontinuous coefficients, Boll. Unione Mat. Ital., 2 (2009), 285-297. | MR 2493657 | Zbl 1178.35367
,[2] 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. | MR 1990295 | Zbl 1034.35032
,[3] 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 1645710
- - ,[4] Existence results via regularity for some nonlinear elliptic problems, Comm. P.D.E., 14 (1989), 663-680. | MR 993824 | Zbl 0678.35035
- ,[5] 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. | MR 2461806 | Zbl 1369.35017
- ,[6] Existence and regularity of renormalized solutions for some elliptic problems involving derivatives of nonlinear terms, J. Diff. Eq., 106 (1993), 215-237. | MR 1251852 | Zbl 0803.35046
- - - ,[7] Unicité de la solution pour des equations elliptiques non linéaires, C. R. Acad. Sc. Paris, 315 (1992), 1159-1164. | MR 1194509
- - ,[8] Almost everywhere convergence of the gradients of solutions to elliptic and parabolic equations, Nonlinear Anal TMA, 19 (1992), 581- 597. | MR 1183665 | Zbl 0783.35020
- ,[9] Existence of bounded solutions for nonlinear elliptic unilateral problems, Ann. Mat. Pura Appl., 152 (1988), 183-196. | MR 980979 | Zbl 0687.35042
- - ,[10] Equations et inéquations non linéaires dans les espaces vectoriels en dualité, Ann. Inst. Fourier (Grenoble), 18 (1968), 115-175. | MR 270222 | Zbl 0169.18602
,[11] XVI, American Mathematical Society, Providence (1970), 1-60. | MR 269962
, Existence theorems for nonlinear partial differential equations, Proceedings of Symposia in Pure Mathematics, vol.[12] Uniqueness results for pseudomonotone problems with , C. R. Math. Acad. Sci. Paris, 344 (2007), 487-492. | MR 2324483 | Zbl 1118.35307
- - ,[13] 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. | MR 194733 | Zbl 0132.10502
- ,[14] I problemi al contorno per le equazioni differenziali di tipo ellittico, Ann. Scuola Norm. Sup. Pisa, 12 (1958), 247-358. | MR 123818
- ,[15] Existence and uniquesness for elliptic equations with lower-order terms, Adv. Calc. Var., 4 (2011), 421-444. | MR 2844512 | Zbl 1232.35051
,[16] Some regularity results for solutions to Dirichlet problems with discontinuous coefficients, preprint. | Zbl 1303.35032
,[17] Le probléme de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus, Ann. Inst. Fourier (Grenoble), 15 (1965), 189-258. | MR 192177 | Zbl 0151.15401
,[18] Existence and uniqueness for nonlinear elliptic equations with lower-order terms, Nonlinear Anal., 75 (2012), 899-912. | MR 2847465 | Zbl 1235.35102
,