On the Lower Semicontinuity of Supremal Functionals

Michele Gori; Francesco Maggi

ESAIM: Control, Optimisation and Calculus of Variations (2010)

  • 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 (2010): 135-143. <http://eudml.org/doc/90685>.

@article{Gori2010,
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. },
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.; supremal functionals; level convexity; Mazur lemma},
language = {eng},
month = {3},
pages = {135-143},
publisher = {EDP Sciences},
title = {On the Lower Semicontinuity of Supremal Functionals},
url = {http://eudml.org/doc/90685},
volume = {9},
year = {2010},
}

TY - JOUR
AU - Gori, Michele
AU - Maggi, Francesco
TI - On the Lower Semicontinuity of Supremal Functionals
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/3//
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∞(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.
LA - eng
KW - Supremal functionals; lower semicontinuity; level convexity; Calculus of Variations; Mazur's lemma.; supremal functionals; level convexity; Mazur lemma
UR - http://eudml.org/doc/90685
ER -

References

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