# Γ-convergence and absolute minimizers for supremal functionals

Thierry Champion; Luigi De Pascale; Francesca Prinari

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

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

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topChampion, Thierry, De Pascale, Luigi, and Prinari, Francesca. "Γ-convergence and absolute minimizers for supremal functionals." ESAIM: Control, Optimisation and Calculus of Variations 10.1 (2010): 14-27. <http://eudml.org/doc/90718>.

@article{Champion2010,

abstract = {
In this paper, we prove that the Lp 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.
},

author = {Champion, Thierry, De Pascale, Luigi, Prinari, Francesca},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Supremal functionals; lower semicontinuity; generalized Jensen inequality; absolute minimizer
(AML; local minimizer); Lp approximation. ; supremal functionals; absolute minimizer; local minimizer; approximation},

language = {eng},

month = {3},

number = {1},

pages = {14-27},

publisher = {EDP Sciences},

title = {Γ-convergence and absolute minimizers for supremal functionals},

url = {http://eudml.org/doc/90718},

volume = {10},

year = {2010},

}

TY - JOUR

AU - Champion, Thierry

AU - De Pascale, Luigi

AU - Prinari, Francesca

TI - Γ-convergence and absolute minimizers for supremal functionals

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2010/3//

PB - EDP Sciences

VL - 10

IS - 1

SP - 14

EP - 27

AB -
In this paper, we prove that the Lp 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.

LA - eng

KW - Supremal functionals; lower semicontinuity; generalized Jensen inequality; absolute minimizer
(AML; local minimizer); Lp approximation. ; supremal functionals; absolute minimizer; local minimizer; approximation

UR - http://eudml.org/doc/90718

ER -

## References

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