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On the lower semicontinuity of supremal functionals. (English) Zbl 1066.49010
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:
49J45Optimal control problems involving semicontinuity and convergence; relaxation
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References:
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