Geodesic
Quantitative estimates on the periodic approximation of the corrector in stochastic homogenization
Antoine Gloria1 ; Félix Otto2
1Université Libre de Bruxelles (ULB), Brussels, Belgium & Team MEPHYSTO, Inria Lille - Nord Europe, Villeneuve d’Ascq, France,
2Max Planck Institute for Mathematics in the Sciences, Inselstr. 22, 04103 Leipzig, Germany,
ESAIM. Proceedings, Tome 48 (2015), pp. 80-97
Cet article a éte moissonné depuis la source EDP Sciences

Voir la notice de l'article

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.
DOI : 10.1051/proc/201448003

Antoine Gloria  1   ; Félix Otto  2

1 Université Libre de Bruxelles (ULB), Brussels, Belgium & Team MEPHYSTO, Inria Lille - Nord Europe, Villeneuve d’Ascq, France,
2 Max Planck Institute for Mathematics in the Sciences, Inselstr. 22, 04103 Leipzig, Germany, 
@article{EP_2015_48_a3,
     author = {Antoine Gloria and F\'elix Otto},
     title = {Quantitative estimates on the periodic approximation of the corrector in stochastic homogenization},
     journal = {ESAIM. Proceedings},
     pages = {80--97},
     year = {2015},
     volume = {48},
     doi = {10.1051/proc/201448003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/201448003/}
}
TY  - JOUR
AU  - Antoine Gloria
AU  - Félix Otto
TI  - Quantitative estimates on the periodic approximation of the corrector in stochastic homogenization
JO  - ESAIM. Proceedings
PY  - 2015
SP  - 80
EP  - 97
VL  - 48
UR  - http://geodesic.mathdoc.fr/articles/10.1051/proc/201448003/
DO  - 10.1051/proc/201448003
LA  - en
ID  - EP_2015_48_a3
ER  - 
%0 Journal Article
%A Antoine Gloria
%A Félix Otto
%T Quantitative estimates on the periodic approximation of the corrector in stochastic homogenization
%J ESAIM. Proceedings
%D 2015
%P 80-97
%V 48
%U http://geodesic.mathdoc.fr/articles/10.1051/proc/201448003/
%R 10.1051/proc/201448003
%G en
%F EP_2015_48_a3
Antoine Gloria; Félix Otto. Quantitative estimates on the periodic approximation of the corrector in stochastic homogenization. ESAIM. Proceedings, Tome 48 (2015), pp. 80-97. doi: 10.1051/proc/201448003

Cité par Sources :