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Homogenization of systems with equi-integrable coefficients

Published online by Cambridge University Press:  08 August 2014

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.

Type
Research Article
Copyright
© EDP Sciences, SMAI, 2014

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References

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