Multivalued Equations on a Bounded Domain via Minimization on Orlicz-Sobolev Spaces

M. L. Carvalho ; J. V. Goncalves

Journal of convex analysis, Tome 21 (2014) no. 1, pp. 201-218.

Résumé

We exploit minimization of locally Lipschitz functionals defined on Orlicz-Sobolev spaces along with convexity techniques, to investigate existence of solution of the multivalued equation\ \ $-\Delta_{\Phi} u \in \partial j(.,u) + h$\ \ in $\Omega$, where $\Omega \subset {\bf R}^N$ is a bounded smooth domain, $\Phi: {\bf R} \to [0,\infty)$ is an N-function, $\Delta_{\Phi}$ is the corresponding $\Phi$-Laplacian, $h$ is a measure on $\Omega$ and $\partial j(., u)$ stands for the Clarke generalized gradient of a function $j$ linked with critical growth. Regularity of the solutions is addressed as well.

Détail

Mots-clés : Minimization, convexity, Orlicz-Sobolev space