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Homogenization of systems with equi-integrable coefficients

 

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Opened Access Homogenization of systems with equi-integrable coefficients
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Author: Briane, Marc
Casado Díaz, Juan
Department: Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico
Date: 2014
Published in: ESAIM: Control, Optimisation and Calculus of Variations, 20 (4), 1214-1223.
Document type: Article
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.
Cite: Briane, M. y Casado Díaz, J. (2014). Homogenization of systems with equi-integrable coefficients. ESAIM: Control, Optimisation and Calculus of Variations, 20 (4), 1214-1223.
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URI: http://hdl.handle.net/11441/42101

DOI: http://dx.doi.org/10.1051/cocv/2014013

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