Calculus of Variations and Geometric Measure Theory
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M. Gori - F. Maggi

On the Lower Semicontinuity of Supremal Functionals

created on 10 Dec 2001
modified by maggi on 19 Dec 2005

[BibTeX]

Published Paper

Inserted: 10 dec 2001
Last Updated: 19 dec 2005

Journal: ESAIM: COCV
Volume: 9
Pages: 135-143
Year: 2003

Abstract:

In this paper we study the lower semicontinuity problem for a supremal functional of the form $F(u,\Omega)=\left
\left
f(x,u,Du)\right
\right
_{L^{\infty}(\Omega)}$ with respect to the strong convergence in $L^{\infty }( \Omega )$, furnishing a comparison with the analogous theory developed by Serrin for integrals. A sort of Mazur's Lemma for gradients of uniformly converging sequences is proved.

Keywords: Supremal functionals, semicontinuity

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