Quantitative estimates on the periodic approximation of the corrector in stochastic homogenization

Quantitative estimates on the periodic approximation of the corrector in stochastic homogenization

We establish quantitative results on the periodic approximation of the corrector equation for the stochastic homogenization of linear elliptic equations in divergence form, when the diffusion coefficients satisfy a spectral gap estimate in probability, and for d> 2...

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Main Authors: Gloria Antoine, Otto Félix
Format: Article
Language:English
Published: EDP Sciences 2015-01-01
Series:ESAIM: Proceedings and Surveys
Online Access:http://dx.doi.org/10.1051/proc/201448003
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spelling doaj-9850b84045f44ca798d91041989f31292021-07-15T14:10:26ZengEDP SciencesESAIM: Proceedings and Surveys2267-30592015-01-0148809710.1051/proc/201448003proc144803Quantitative estimates on the periodic approximation of the corrector in stochastic homogenizationGloria Antoine0Otto Félix1Université Libre de Bruxelles (ULB), Brussels, Belgium & Team MEPHYSTO, Inria Lille - Nord EuropeMax Planck Institute for Mathematics in the Sciences, Inselstr. 22We establish quantitative results on the periodic approximation of the corrector equation for the stochastic homogenization of linear elliptic equations in divergence form, when the diffusion coefficients satisfy a spectral gap estimate in probability, and for d> 2. This work is based on [5], which is a complete continuum version of [6, 7] (with in addition optimal results for d = 2). The main difference with respect to the first part of [5] is that we avoid here the use of Green’s functions and more directly rely on the De Giorgi-Nash-Moser theory.http://dx.doi.org/10.1051/proc/201448003
collection DOAJ
language English
format Article
sources DOAJ
author Gloria Antoine
Otto Félix
spellingShingle Gloria Antoine
Otto Félix
Quantitative estimates on the periodic approximation of the corrector in stochastic homogenization
ESAIM: Proceedings and Surveys
author_facet Gloria Antoine
Otto Félix
author_sort Gloria Antoine
title Quantitative estimates on the periodic approximation of the corrector in stochastic homogenization
title_short Quantitative estimates on the periodic approximation of the corrector in stochastic homogenization
title_full Quantitative estimates on the periodic approximation of the corrector in stochastic homogenization
title_fullStr Quantitative estimates on the periodic approximation of the corrector in stochastic homogenization
title_full_unstemmed Quantitative estimates on the periodic approximation of the corrector in stochastic homogenization
title_sort quantitative estimates on the periodic approximation of the corrector in stochastic homogenization
publisher EDP Sciences
series ESAIM: Proceedings and Surveys
issn 2267-3059
publishDate 2015-01-01
description We establish quantitative results on the periodic approximation of the corrector equation for the stochastic homogenization of linear elliptic equations in divergence form, when the diffusion coefficients satisfy a spectral gap estimate in probability, and for d> 2. This work is based on [5], which is a complete continuum version of [6, 7] (with in addition optimal results for d = 2). The main difference with respect to the first part of [5] is that we avoid here the use of Green’s functions and more directly rely on the De Giorgi-Nash-Moser theory.
url http://dx.doi.org/10.1051/proc/201448003
work_keys_str_mv AT gloriaantoine quantitativeestimatesontheperiodicapproximationofthecorrectorinstochastichomogenization
AT ottofelix quantitativeestimatesontheperiodicapproximationofthecorrectorinstochastichomogenization
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