Regularity theorems for random elliptic operators on domains
Abstract
Regularity theorems \`a 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 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.
Keywords
Cite
@article{arxiv.2604.01209,
title = {Regularity theorems for random elliptic operators on domains},
author = {Peter Bella and Julian Fischer and Marc Josien and Claudia Raithel},
journal= {arXiv preprint arXiv:2604.01209},
year = {2026}
}
Comments
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