On the lower semicontinuity of supremal functionals
ESAIM: Control, Optimisation and Calculus of Variations, Volume 9 (2003), pp. 135-143.

In this paper we study the lower semicontinuity problem for a supremal functional of the form $F\left(u,\Omega \right)=\underset{x\in \Omega }{\mathrm{ess}\phantom{\rule{0.166667em}{0ex}}\mathrm{sup}}f\left(x,u\left(x\right),Du\left(x\right)\right)$ with respect to the strong convergence in ${L}^{\infty }\left(\Omega \right)$, 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.

DOI: 10.1051/cocv:2003005
Classification: 49J45,  49L25
Keywords: supremal functionals, lower semicontinuity, level convexity, calculus of variations, Mazur's lemma
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Gori, Michele; Maggi, Francesco. On the lower semicontinuity of supremal functionals. ESAIM: Control, Optimisation and Calculus of Variations, Volume 9 (2003), pp. 135-143. doi : 10.1051/cocv:2003005. http://www.numdam.org/articles/10.1051/cocv:2003005/

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