Calculus of Variations and Geometric Measure Theory

T. Champion - L. De Pascale - F. Prinari

Semicontinuity ad Absolute Minimizers for Supremal Functionals

created on 20 Jun 2002
modified by depascal on 22 Jun 2005


Published Paper

Inserted: 20 jun 2002
Last Updated: 22 jun 2005

Journal: ESAIM Control Optim. Calc. Var.
Volume: 10
Number: 1
Pages: 14-27
Year: 2004

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In this paper, we prove a semi-continuity theorem for supremal functionals whose supremand satisfies weak coercivity assumptions as well as a generalized Jensen inequality. The existence of minimizers for variational problems involving such functionals (together with a Dirichlet condition) easily follows from this result. We show the existence of at least one absolute minimizer ({\it i.e.} local solution) among these minimizers. We provide two different proofs of this fact relying on different assumptions and techniques.