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arXiv · 2604.01209

Regularity theorems for random elliptic operators on domains

Peter Bella·Julian Fischer·Marc Josien·Claudia Raithel
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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 $C^{1,\alpha}$ 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.

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Peter Bella, Julian Fischer, Marc Josien, Claudia Raithel. 2026-04-01. Regularity theorems for random elliptic operators on domains. https://arxiv.org/abs/2604.01209

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