Volume 20, Number 4, October-December 2014
|Page(s)||1214 - 1223|
|Published online||08 August 2014|
Homogenization of systems with equi-integrable coefficients
Institut de Recherche Mathématique de Rennes, INSA de Rennes,
2 Departemento. de Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Spain
Received: 1 October 2013
Revised: 1 February 2014
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.
Mathematics Subject Classification: 35B27 / 49K20
Key words: Homogenization / vector-valued systems / not equi-bounded coefficients / equi-integrable coefficients / H-convergence
© EDP Sciences, SMAI, 2014
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