Homogenization of periodic nonconvex integral functionals in terms of Young measures

Issue		ESAIM: COCV Volume 12, Number 1, January 2006


Page(s)		35 - 51
DOI		10.1051/cocv:2005031
Published online		15 December 2005

ESAIM: COCV, January 2006, Vol. 12, pp. 35-51
DOI: 10.1051/cocv:2005031

Homogenization of periodic nonconvex integral functionals in terms of Young measures

Omar Anza Hafsa¹, Jean-Philippe Mandallena^{2, 3} and Gérard Michaille^{2, 3}

¹ Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland; anza@math.unizh.ch
² EMIAN (Équipe de Mathématiques, d'Informatiques et Applications de Nîmes), Centre Universitaire de Formation et de Recherche de Nîmes, Site des Carmes, Place Gabriel Péri, Cedex 01, 30021 Nîmes, France; jean-philippe.mandallena@unimes.fr
³ I3M (Institut de Mathématiques et Modélisation de Montpellier) UMR-CNRS 5149, Université Montpellier II, Place Eugène Bataillon, 34090 Montpellier, France; micha@math.univ-montp2.fr

(Received June 4, 2004. Revised February 16, 2005. / Published online: 15 December 2005)

Abstract
Homogenization of periodic functionals, whose integrands possess possibly multi-well structure, is treated in terms of Young measures. More precisely, we characterize the $\Gamma$ -limit of sequences of such functionals in the set of Young measures, extending the relaxation theorem of Kinderlherer and Pedregal. We also make precise the relationship between our homogenized density and the classical one.

Mathematics Subject Classification. 35B27, 49J45, 74N15.

Key words: Young measures, homogenization.

© EDP Sciences, SMAI 2006

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