
Journal of Convex Analysis 14 (2007), No. 3, 465477 Copyright Heldermann Verlag 2007 Differential Inclusions in SBV_{0}(Ω) and Applications to the Calculus of Variations José Matias Dep. de Matemática, Instituto Superior Técnico, Av. Rovisco Pais 1, 1049001 Lisboa, Portugal jmatias@math.ist.utl.pt [Abstractpdf] We study necessary and sufficient conditions for the existence of solutions in $SBV_0(\Omega)$ of a variational problem involving only bulk energy. Related to that we study the problem of finding $u \in SBV_0(\Omega)$ such that $$\nabla u (x)\in E,\text{ a.e. in } \Omega,$$ subject to the condition $$\int \nabla u = \zeta_0 \Omega,$$ where $E\subseteq \mathbb{R}^N$ is a given set and $\zeta_0 \in $ int co $E$ is prescribed. [ Fulltextpdf (144 KB)] for subscribers only. 