Dimensional reduction for supremal functionals

Jean-François Babadjian; Francesca Prinari; Elvira Zappale

doi:10.3934/dcds.2012.32.1503

Article Contents

2012, Volume 32, Issue 5: 1503-1535. Doi: 10.3934/dcds.2012.32.1503

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Dimensional reduction for supremal functionals

1.
Université Pierre et Marie Curie – Paris 6, CNRS, UMR 7598, Laboratoire Jacques-Louis Lions, 75005 Paris
2.
Dipartimento di Matematica, Università di Ferrara, Via Machiavelli, 35, 44100, Ferrara
3.
DIEII, Università degli Studi di Salerno, Via Ponte Don Melillo, 84084 Fisciano

Received: October 31, 2010

Revised: April 30, 2011

Published: April 2012

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Abstract

A 3D-2D dimensional reduction analysis for supremal functionals is performed in the realm of $\Gamma^*$-convergence. We show that the limit functional still admits a supremal representation, and we provide a precise identification of its density in some particular cases. Our results rely on an abstract representation theorem for the $\Gamma^*$-limit of a family of supremal functionals.

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Mathematics Subject Classification: 49J45, 74K99, 74Q99.

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