Γ -convergence and absolute minimizers for supremal functionals

Thierry Champion; Luigi De Pascale; Francesca Prinari

ESAIM: Control, Optimisation and Calculus of Variations (2004)

  • Volume: 10, Issue: 1, page 14-27
  • ISSN: 1292-8119

Abstract

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In this paper, we prove that the L p approximants naturally associated to a supremal functional Γ -converge to it. This yields a lower semicontinuity result for supremal functionals whose supremand satisfy weak coercivity assumptions as well as a generalized Jensen inequality. The existence of minimizers for variational problems involving such functionals (together with a Dirichlet condition) then easily follows. In the scalar case we show the existence of at least one absolute minimizer (i.e. local solution) among these minimizers. We provide two different proofs of this fact relying on different assumptions and techniques.

How to cite

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Champion, Thierry, Pascale, Luigi De, and Prinari, Francesca. "$\Gamma $-convergence and absolute minimizers for supremal functionals." ESAIM: Control, Optimisation and Calculus of Variations 10.1 (2004): 14-27. <http://eudml.org/doc/245585>.

@article{Champion2004,
abstract = {In this paper, we prove that the $L^p$ approximants naturally associated to a supremal functional $\Gamma $-converge to it. This yields a lower semicontinuity result for supremal functionals whose supremand satisfy weak coercivity assumptions as well as a generalized Jensen inequality. The existence of minimizers for variational problems involving such functionals (together with a Dirichlet condition) then easily follows. In the scalar case we show the existence of at least one absolute minimizer (i.e. local solution) among these minimizers. We provide two different proofs of this fact relying on different assumptions and techniques.},
author = {Champion, Thierry, Pascale, Luigi De, Prinari, Francesca},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {supremal functionals; lower semicontinuity; generalized Jensen inequality; absolute minimizer (AML; local minimizer); $L^p$ approximation; absolute minimizer; local minimizer; approximation},
language = {eng},
number = {1},
pages = {14-27},
publisher = {EDP-Sciences},
title = {$\Gamma $-convergence and absolute minimizers for supremal functionals},
url = {http://eudml.org/doc/245585},
volume = {10},
year = {2004},
}

TY - JOUR
AU - Champion, Thierry
AU - Pascale, Luigi De
AU - Prinari, Francesca
TI - $\Gamma $-convergence and absolute minimizers for supremal functionals
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 2004
PB - EDP-Sciences
VL - 10
IS - 1
SP - 14
EP - 27
AB - In this paper, we prove that the $L^p$ approximants naturally associated to a supremal functional $\Gamma $-converge to it. This yields a lower semicontinuity result for supremal functionals whose supremand satisfy weak coercivity assumptions as well as a generalized Jensen inequality. The existence of minimizers for variational problems involving such functionals (together with a Dirichlet condition) then easily follows. In the scalar case we show the existence of at least one absolute minimizer (i.e. local solution) among these minimizers. We provide two different proofs of this fact relying on different assumptions and techniques.
LA - eng
KW - supremal functionals; lower semicontinuity; generalized Jensen inequality; absolute minimizer (AML; local minimizer); $L^p$ approximation; absolute minimizer; local minimizer; approximation
UR - http://eudml.org/doc/245585
ER -

References

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