Weighted Meyers estimates in perforated domains

TL;DR

This paper develops advanced Meyers estimates and regularity results for solutions in perforated domains, incorporating probabilistic methods to handle randomness and ergodicity in the perforation structure.

Contribution

It introduces weighted Meyers estimates and a hypercontractivity property for correctors under stochastic perforation models with weaker ergodic assumptions.

Findings

Established Meyers estimates in perforated domains

Proved hypercontractivity of correctors under stochastic conditions

Linked regularity results with probabilistic ergodic properties

Abstract

The present work aims to provide Meyers estimates throughout a finer inner regularity theory in perforated domains. We also provide a hypercontractivity property on correctors whenever the perforations are controlled with a uniformly bounded random variable and the underlying probability space admits a weaker form of ergodicity which we called coarsened logarithmic Sobolev inequality.