• Citer

Quantitative results on the corrector equation in stochastic homogenization

par Gloria, Antoine ;Otto, Felix
Référence Journal of the European Mathematical Society, 19, 11, page (3489-3548)
Publication Publié, 2017

Article révisé par les pairs

• Accès en ligne
• Détails
• Contenu
• Statistiques

Résumé :

We derive optimal estimates in stochastic homogenization of linear elliptic equations in divergence form in dimensions d≥2. In previous works we studied the model problem of a discrete elliptic equation on Zd . 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.