Journal of Convex Analysis 21 (2014), No. 1, 201--218
Copyright 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.
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