On the lower semicontinuity of supremal functionals

Michele Gori; Francesco Maggi

ESAIM: Control, Optimisation and Calculus of Variations (2003)

  • Volume: 9, page 135-143
  • ISSN: 1292-8119

Abstract

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In this paper we study the lower semicontinuity problem for a supremal functional of the form F ( u , Ω ) = ess sup x ∈ Ω f ( x , u ( x ) , D u ( 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.

How to cite

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Gori, Michele, and Maggi, Francesco. "On the lower semicontinuity of supremal functionals." ESAIM: Control, Optimisation and Calculus of Variations 9 (2003): 135-143. <http://eudml.org/doc/245720>.

@article{Gori2003,
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 $L^\infty (\Omega )$, 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.},
author = {Gori, Michele, Maggi, Francesco},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {supremal functionals; lower semicontinuity; level convexity; calculus of variations; Mazur’s lemma; Mazur lemma},
language = {eng},
pages = {135-143},
publisher = {EDP-Sciences},
title = {On the lower semicontinuity of supremal functionals},
url = {http://eudml.org/doc/245720},
volume = {9},
year = {2003},
}

TY - JOUR
AU - Gori, Michele
AU - Maggi, Francesco
TI - On the lower semicontinuity of supremal functionals
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 2003
PB - EDP-Sciences
VL - 9
SP - 135
EP - 143
AB - 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 $L^\infty (\Omega )$, 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.
LA - eng
KW - supremal functionals; lower semicontinuity; level convexity; calculus of variations; Mazur’s lemma; Mazur lemma
UR - http://eudml.org/doc/245720
ER -

References

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