Homogenization of systems with equi-integrable coefficients
Marc Briane, Juan Casado‐Díaz · ESAIM Control Optimisation and Calculus of Variations · 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 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.