Coarsen entropy inequalities and its applications in quantitative stochastic homogenization

TL;DR

This paper investigates entropy inequalities under decorrelation assumptions at large scales and applies these results to weighted Meyers estimates in perforated domains, leading to hypercontractivity of Neumann boundary condition correctors.

Contribution

It introduces new entropy inequalities applicable at large scales and demonstrates their use in deriving hypercontractivity for correctors with Neumann boundary conditions.

Findings

Entropy inequalities hold under large-scale decorrelation assumptions.

Weighted Meyers estimates are established in perforated domains.

Hypercontractivity of Neumann boundary condition correctors is proven.

Abstract

In this work, we study the validity of Entropy inequalities under decorrelation assumptions at large-scales, and also we study the problem of Weighted Meyers estimate in perforated domains. As a consequence, we obtain the hypercontractivity of correctors with Neumann boundary conditions.