The Corrector in Stochastic Homogenization: Near-Optimal Rates With Optimal Stochastic Integrability
Antoine Gloria, Félix Otto · arXiv (Cornell University) · 2015
Abstract. We consider uniformly elliptic coefficient fields that are randomly distributed according to a stationary ensemble of a finite range of dependence. We show that the gradient ∇φ of the corrector φ, when spatially averaged over a scale R 1 decays like R−α for any α < d2. We establish these rates on the level of Gaussian bounds in terms of the stochastic integrability.