Abstract

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 −ΔΦu∈∂j(.,u)+h-\Delta_{\Phi} u \in \partial j(.,u) + h in Ω\Omega, where Ω⊂RN\Omega \subset {\bf R}^N is a bounded smooth domain, Φ:R→[0,∞)\Phi: {\bf R} \to [0,\infty) is an N-function, ΔΦ\Delta_{\Phi} is the corresponding Φ\Phi-Laplacian, hh is a measure on Ω\Omega and ∂j(.,u)\partial j(., u) stands for the Clarke generalized gradient of a function jj linked with critical growth. Regularity of the solutions is addressed as well.

Author information

Contact details are reproduced from the original publication and may be historical.

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

Keywords

  • Minimization
  • convexity
  • Orlicz-Sobolev space

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Suggested citation

M. L. Carvalho, J. V. Goncalves. “Multivalued Equations on a Bounded Domain via Minimization on Orlicz-Sobolev Spaces.” Journal of Convex Analysis 21 (2014), No. 1, 201–218. https://doi.org/10.68381/jca21011

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Published by Heldermann Verlag, 2014. Rights now held by Banach Press LLC.