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not equi-bounded coefficients

ESAIM: Control, Optimisation and Calculus of Variations (1)

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Homogenization of systems with equi-integrable coefficients
Marc Briane, Juan Casado-Díaz
Journal:

ESAIM: Control, Optimisation and Calculus of Variations / Volume 20 / Issue 4 / October 2014

Published online by Cambridge University Press:

08 August 2014, pp. 1214-1223

Print publication:

October 2014
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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.