Weighted Meyers estimates in perforated domains

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. Contents 1 Preliminaries 42 Proof of the main results 10 3 C 1,1 regularity of harmonic maps 16