Regularity theorems for random elliptic operators on domains

Abstract

Regularity theorems à la Avellaneda-Lin are an indispensable part of the modern quantitative theory of stochastic homogenization. While interior regularity results for random elliptic operators have been available for a while, on general smooth domains the existing theory has until recently remained limited to Lipschitz estimates. We establish $C^{1,\hat{I}\pm }$ regularity results for random elliptic operators on bounded sufficiently smooth domains, as well as for scalar problems on convex polytopes. We, furthermore, prove a number of auxiliary results typically employed in the derivation of fluctuation bounds, such as a weighted Meyers estimate.

33 pages, The results in this article have been split off from the first version of arXiv:2403.12911. It is, in particular, a companion of arXiv:2403.12911v2