| Issue |
ESAIM: COCV
Volume 9, February 2003
|
|
|---|---|---|
| Page(s) | 135 - 143 | |
| DOI | https://doi.org/10.1051/cocv:2003005 | |
| Published online | 15 September 2003 | |
On the Lower Semicontinuity of Supremal Functionals
1
Dipartimento di Matematica “L. Tonelli”, Università di Pisa,
Via Buonarroti 2, 56127 Pisa, Italy; gori@mail.dm.unipi.it.
2
Dipartimento di Matematica “U. Dini”, Università di Firenze,
Viale Morgagni 67/A, 50134 Firenze, Italy; maggi@math.unifi.it.
Received:
29
July
2002
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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