Abstract

We study necessary and sufficient conditions for the existence of solutions in SBV0(Ω)SBV_0(\Omega) of a variational problem involving only bulk energy. Related to that we study the problem of finding u∈SBV0(Ω)u \in SBV_0(\Omega) such that ∇u(x)∈E, a.e. in Ω,\nabla u (x)\in E,\text{ a.e. in } \Omega, subject to the condition ∫∇u=ζ0∣Ω∣,\int \nabla u = \zeta_0 |\Omega|, where E⊆RNE\subseteq \mathbb{R}^N is a given set and ζ0∈\zeta_0 \in int co EE is prescribed

Author information

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José Matias

Dep. de Matemática, Instituto Superior Técnico, Av. Rovisco Pais 1, 1049-001 Lisboa, Portugal

jmatias@math.ist.utl.pt

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Suggested citation

J. Matias. “Differential Inclusions in SBV_0(Ω) and Applications to the Calculus of Variations.” Journal of Convex Analysis 14 (2007), No. 3, 465–477. https://doi.org/10.68381/jca14030

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Published by Heldermann Verlag, 2007. Rights now held by Banach Press LLC.