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Homogenization of periodic nonconvex integral functionals in terms of Young measures

Published online by Cambridge University Press:  15 December 2005

Omar Anza Hafsa ,
Jean-Philippe Mandallena  and
Gérard Michaille
Omar Anza Hafsa
Affiliation:
Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland; anza@math.unizh.ch
Jean-Philippe Mandallena
Affiliation:
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 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
Gérard Michaille
Affiliation:
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 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
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Abstract

Homogenization of periodic functionals, whose integrands possess possibly multi-well structure, is treated in terms of Young measures. More precisely, we characterize the Γ-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.

Keywords

Young measureshomogenization.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 12 , Issue 1 , January 2006 , pp. 35 - 51
Copyright
© EDP Sciences, SMAI, 2006

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