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Zbl 1066.49010
Gori, Michele; Maggi, Francesco
On the lower semicontinuity of supremal functionals. (English)
[J] ESAIM, Control Optim. Calc. Var. 9, 135-143 (2003). ISSN 1292-8119; ISSN 1262-3377/e

Summary: In this paper we study the lower semicontinuity problem for a supremal functional of the form $$F(u,\Omega )= \underset {x\in \Omega } \to {\text{ess\,sup}} f(x,u(x),Du(x))$$ 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.

MSC 2000:: *49J45 Optimal control problems inv. semicontinuity and convergence

Keywords: supremal functionals; lower semicontinuity; level convexity; Mazur lemma

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