Volume 9, March 2003
|Page(s)||135 - 143|
|Published online||15 September 2003|
On the Lower Semicontinuity of Supremal Functionals
Dipartimento di Matematica “L. Tonelli”, Università di Pisa,
Via Buonarroti 2, 56127 Pisa, Italy; email@example.com.
2 Dipartimento di Matematica “U. Dini”, Università di Firenze, Viale Morgagni 67/A, 50134 Firenze, Italy; firstname.lastname@example.org.
In this paper we study the lower semicontinuity problem for a supremal functional of the form 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.
Mathematics Subject Classification: 49J45 / 49L25
Key words: Supremal functionals / lower semicontinuity / level convexity / Calculus of Variations / Mazur's lemma.
© EDP Sciences, SMAI, 2003
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