Homogenization of systems with equi-integrable coefficients

Marc Briane; Juan Casado-Díaz

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

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

Abstract

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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.

How to cite

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Briane, 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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