Geodesic
Homogenization of systems with equi-integrable coefficients
ESAIM: Control, Optimisation and Calculus of Variations, Tome 20 (2014) no. 4, pp. 1214-1223

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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.

DOI : 10.1051/cocv/2014013
Classification : 35B27, 49K20
Keywords: homogenization, vector-valued systems, not equi-bounded coefficients, equi-integrable coefficients, H-convergence 
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     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},
     publisher = {EDP-Sciences},
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     language = {en},
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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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