Journal Home Page Cumulative Index List of all Volumes Complete Contentsof this Volume Previous Article Journal of Convex Analysis 21 (2014), No. 1, 201--218Copyright Heldermann Verlag 2014 Multivalued Equations on a Bounded Domain via Minimization on Orlicz-Sobolev Spaces M. L. Carvalho Universidade Federal de Goiás, Dep. de Matemática, 75804-020 Jataí, GO, Brasil J. V. Goncalves Universidade Federal de Goiás, Inst. de Matemática e Estatística, 74001-970 Goiânia, GO, Brasil goncalves.jva@gmail.com [Abstract-pdf] 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. Keywords: Minimization, convexity, Orlicz-Sobolev space. [ Fulltext-pdf  (167  KB)] for subscribers only.