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On the Lower Semicontinuity of Supremal Functionals

Published online by Cambridge University Press:  15 September 2003

Michele Gori  and
Francesco Maggi
Michele Gori
Affiliation:
Dipartimento di Matematica “L. Tonelli”, Università di Pisa, Via Buonarroti 2, 56127 Pisa, Italy; [email protected].
Francesco Maggi
Affiliation:
Dipartimento di Matematica “U. Dini”, Università di Firenze, Viale Morgagni 67/A, 50134 Firenze, Italy; [email protected].
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Abstract

In this paper we study the lower semicontinuity problem for a supremal functional of the form $F(u,\Omega )= \underset{x\in\Omega}{\rm ess\,sup} f(x,u(x),Du(x))$ with respect to the strong convergence in L∞(Ω), 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 functionalslower semicontinuitylevel convexityCalculus of VariationsMazur's lemma.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 9 , January 2003 , pp. 135 - 143
Copyright
© EDP Sciences, SMAI, 2003

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