Quantitative estimates on the periodic approximation of the corrector in stochastic homogenization
Antoine Gloria, Félix Otto · ESAIM Proceedings and Surveys · 2015
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.