Title :

Quantitative results on the corrector equation in stochastic homogenization

Author(s) :

Gloria, Antoine [Auteur]
Laboratoire Jacques-Louis Lions [LJLL (UMR_7598)]
Quantitative methods for stochastic models in physics [MEPHYSTO]
Département de Mathématique [Bruxelles] [ULB]
Otto, Felix [Auteur]
Max Planck Institute for Mathematics in the Sciences [MPI-MiS]

Journal title :

Journal of the European Mathematical Society

Pages :

3489-3548

Publisher :

European Mathematical Society

Publication date :

2017

ISSN :

1435-9855

English keyword(s) :

Stochastic homogenization
corrector equation
variance estimate

HAL domain(s) :

Mathématiques [math]/Equations aux dérivées partielles [math.AP]
Mathématiques [math]/Probabilités [math.PR]

English abstract : [en]

We derive optimal estimates in stochastic homogenization of linear elliptic equations in divergence form in dimensions $d\ge 2$. In previous works we studied the model problem of a discrete elliptic equation on $\mathbb{Z}^d$. ...
Show more >We derive optimal estimates in stochastic homogenization of linear elliptic equations in divergence form in dimensions $d\ge 2$. In previous works we studied the model problem of a discrete elliptic equation on $\mathbb{Z}^d$. Under the assumption that a spectral gap estimate holds in probability, we proved that there exists a stationary corrector field in dimensions $d>2$ and that the energy density of that corrector behaves as if it had finite range of correlation in terms of the variance of spatial averages - the latter decays at the rate of the central limit theorem. In this article we extend these results, and several other estimates, to the case of a continuum linear elliptic equation whose (not necessarily symmetric) coefficient field satisfies a continuum version of the spectral gap estimate. In particular, our results cover the example of Poisson random inclusions.Show less >

Language :

Anglais

Popular science :

Non

European Project :

QUANTHOM

Comment :

1 figure

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL