Weighted Meyers estimates in perforated domains

2020/07/22 by Anderson Melchor Hernandez, Hernandez, Anderson M.
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2007.12003

openalex publication_date 2020/07/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• The structure of fluctuations in stochastic homogenization
• Quantitative estimates for homogenization of nonlinear elliptic operators in perforated domains

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• Annealed Calderón-Zygmund estimates for elliptic operators with random coefficients on C¹ domains
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