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Homogenization of systems with equi-integrable coefficients

Published online by Cambridge University Press:  08 August 2014

Marc Briane  and
Juan Casado-Díaz
Marc Briane
Affiliation:
Institut de Recherche Mathématique de Rennes, INSA de Rennes, France. mbriane@insa-rennes.fr
Juan Casado-Díaz
Affiliation:
Departemento. de Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Spain; jcasadod@us.es
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Abstract

In this paper we prove a H-convergence type result for the homogenization of systems the coefficients of which satisfy a functional ellipticity condition and a strong equi-integrability condition. The equi-integrability assumption allows us to control the fact that the coefficients are not equi-bounded. Since the truncation principle used for scalar equations does not hold for vector-valued systems, we present an alternative approach based on an approximation result by Lipschitz functions due to Acerbi and Fusco combined with a Meyers Lp-estimate adapted to the functional ellipticity condition. The present framework includes in particular the elasticity case and the reinforcement by stiff thin fibers.

Keywords

Homogenizationvector-valued systemsnot equi-bounded coefficientsequi-integrable coefficientsH-convergence
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 20 , Issue 4 , October 2014 , pp. 1214 - 1223
Copyright
© EDP Sciences, SMAI, 2014

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