Journal Home Page Cumulative Index List of all Volumes Complete Contentsof this Volume Previous Article Journal of Convex Analysis 14 (2007), No. 3, 465--477Copyright Heldermann Verlag 2007 Differential Inclusions in SBV0(Ω) and Applications to the Calculus of Variations José Matias Dep. de Matemática, Instituto Superior Técnico, Av. Rovisco Pais 1, 1049-001 Lisboa, Portugal jmatias@math.ist.utl.pt [Abstract-pdf] 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. [ Fulltext-pdf  (144  KB)] for subscribers only.