# Homogenization of systems with equi-integrable coefficients

ESAIM: Control, Optimisation and Calculus of Variations (2014)

- Volume: 20, Issue: 4, page 1214-1223
- ISSN: 1292-8119

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topBriane, Marc, and Casado-Díaz, Juan. "Homogenization of systems with equi-integrable coefficients." ESAIM: Control, Optimisation and Calculus of Variations 20.4 (2014): 1214-1223. <http://eudml.org/doc/272933>.

@article{Briane2014,

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.},

author = {Briane, Marc, Casado-Díaz, Juan},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {homogenization; vector-valued systems; not equi-bounded coefficients; equi-integrable coefficients; H-convergence; Lusin approximation; Meyers inequality; homogeneous Dirichlet boundary conditions},

language = {eng},

number = {4},

pages = {1214-1223},

publisher = {EDP-Sciences},

title = {Homogenization of systems with equi-integrable coefficients},

url = {http://eudml.org/doc/272933},

volume = {20},

year = {2014},

}

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

PB - EDP-Sciences

VL - 20

IS - 4

SP - 1214

EP - 1223

AB - 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.

LA - eng

KW - homogenization; vector-valued systems; not equi-bounded coefficients; equi-integrable coefficients; H-convergence; Lusin approximation; Meyers inequality; homogeneous Dirichlet boundary conditions

UR - http://eudml.org/doc/272933

ER -

## References

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