In this paper we study the lower semicontinuity problem for a supremal functional of the form F(u, Omega) = ess supf(x; u(x);Du(x)) with respect to the strong convergence in L-infinity(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.
On the lower semicontinuity of supremal functionals / M. GORI; F. MAGGI. - In: ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS. - ISSN 1262-3377. - ELETTRONICO. - 9:(2003), pp. 135-143. [10.1051/cocv:2003005]
On the lower semicontinuity of supremal functionals
GORI, MICHELE;MAGGI, FRANCESCO
2003
Abstract
In this paper we study the lower semicontinuity problem for a supremal functional of the form F(u, Omega) = ess supf(x; u(x);Du(x)) with respect to the strong convergence in L-infinity(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.
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