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Integral representation for a class of $C^1$-convex functionals

Gianni Dal Maso·Anneliese Defranceschi·Enrico Vitali
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Abstract

In view of the applications to the asymptotic analysis of a family of obstacle problems, we consider a class of convex local functionals $F(u,A)$, defined for all functions $u$ in a suitable vector valued Sobolev space and for all open sets $A$ in ${\bf R}^n$. Sufficient conditions are given in order to obtain an integral representation of the form $F(u,A)=\int_A f(x,u(x))\,dμ+ ν(A)$, where $μ$ and $ν$ are Borel measures and $f$ is convex in the second variable.

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BibTeXRIS

Gianni Dal Maso, Anneliese Defranceschi, Enrico Vitali. 1992-05-11. Integral representation for a class of $C^1$-convex functionals. https://arxiv.org/abs/funct-an/9205002

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