
Journal of Convex Analysis 21 (2014), No. 1, 201218 Copyright Heldermann Verlag 2014 Multivalued Equations on a Bounded Domain via Minimization on OrliczSobolev Spaces M. L. Carvalho Universidade Federal de Goiás, Dep. de Matemática, 75804020 Jataí, GO, Brasil J. V. Goncalves Universidade Federal de Goiás, Inst. de Matemática e Estatística, 74001970 Goiânia, GO, Brasil goncalves.jva@gmail.com [Abstractpdf] We exploit minimization of locally Lipschitz functionals defined on OrliczSobolev 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 Nfunction, $\Delta_{\Phi}$ 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. Keywords: Minimization, convexity, OrliczSobolev space. [ Fulltextpdf (167 KB)] for subscribers only. 