Work

Regularity theorems for random elliptic operators on domains

Year: 2026

Type: preprint

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 $C^{1,α}$ 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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2604.01209

Authors: Bella, Peter, Fischer, Julian, Josien, Marc, Raithel, Claudia

Institutions: TU Dortmund University, Institute of Science and Technology Austria, Commissariat à l'Énergie Atomique et aux Énergies Alternatives, CEA Cadarache, Hochschule Campus Wien

Topic: Advanced Mathematical Modeling in Engineering

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: European Commission, Deutsche Forschungsgemeinschaft, Austrian Science Fund

Awards: G3602194453, G546635654, Robuste Strukturen in der KomplianzMinimierung

OpenAlex ID: W7148313233

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