Journal of convex analysis, Tome 14 (2007) no. 3, pp. 465-477
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J. Matias. Differential Inclusions in SBV0(Ω) and Applications to the Calculus of Variations. Journal of convex analysis, Tome 14 (2007) no. 3, pp. 465-477. http://geodesic.mathdoc.fr/item/JCA_2007_14_3_JCA_2007_14_3_a1/
@article{JCA_2007_14_3_JCA_2007_14_3_a1,
author = {J. Matias},
title = {Differential {Inclusions} in {SBV\protect\textsubscript{0}(\ensuremath{\Omega})} and {Applications} to the {Calculus} of {Variations}},
journal = {Journal of convex analysis},
pages = {465--477},
year = {2007},
volume = {14},
number = {3},
url = {http://geodesic.mathdoc.fr/item/JCA_2007_14_3_JCA_2007_14_3_a1/}
}
TY - JOUR
AU - J. Matias
TI - Differential Inclusions in SBV0(Ω) and Applications to the Calculus of Variations
JO - Journal of convex analysis
PY - 2007
SP - 465
EP - 477
VL - 14
IS - 3
UR - http://geodesic.mathdoc.fr/item/JCA_2007_14_3_JCA_2007_14_3_a1/
ID - JCA_2007_14_3_JCA_2007_14_3_a1
ER -
%0 Journal Article
%A J. Matias
%T Differential Inclusions in SBV0(Ω) and Applications to the Calculus of Variations
%J Journal of convex analysis
%D 2007
%P 465-477
%V 14
%N 3
%U http://geodesic.mathdoc.fr/item/JCA_2007_14_3_JCA_2007_14_3_a1/
%F JCA_2007_14_3_JCA_2007_14_3_a1
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.
