Homogenization of systems with equi-integrable coefficients

¹ Institut de Recherche Mathématique de Rennes, INSA de Rennes, France
mbriane@insa-rennes.fr
² Departemento. de Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Spain
jcasadod@us.es

Received: 1 October 2013
Revised: 1 February 2014

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 L^p-estimate adapted to the functional ellipticity condition. The present framework includes in particular the elasticity case and the reinforcement by stiff thin fibers.