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.
Keywords: homogenization, vector-valued systems, not equi-bounded coefficients, equi-integrable coefficients, H-convergence
@article{COCV_2014__20_4_1214_0,
author = {Briane, Marc and Casado-D{\'\i}az, Juan},
title = {Homogenization of systems with equi-integrable coefficients},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {1214--1223},
year = {2014},
publisher = {EDP-Sciences},
volume = {20},
number = {4},
doi = {10.1051/cocv/2014013},
mrnumber = {3264240},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2014013/}
}
TY - JOUR AU - Briane, Marc AU - Casado-Díaz, Juan TI - Homogenization of systems with equi-integrable coefficients JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2014 SP - 1214 EP - 1223 VL - 20 IS - 4 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/cocv/2014013/ DO - 10.1051/cocv/2014013 LA - en ID - COCV_2014__20_4_1214_0 ER -
%0 Journal Article %A Briane, Marc %A Casado-Díaz, Juan %T Homogenization of systems with equi-integrable coefficients %J ESAIM: Control, Optimisation and Calculus of Variations %D 2014 %P 1214-1223 %V 20 %N 4 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/cocv/2014013/ %R 10.1051/cocv/2014013 %G en %F COCV_2014__20_4_1214_0
Briane, Marc; Casado-Díaz, Juan. Homogenization of systems with equi-integrable coefficients. ESAIM: Control, Optimisation and Calculus of Variations, Tome 20 (2014) no. 4, pp. 1214-1223. doi: 10.1051/cocv/2014013
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