Quantitative estimates for homogenization of nonlinear elliptic operators in perforated domains

2020/01/16 by Li Wang, Qiang Xu, Wang, Li +3 · 2 citations
Computer Science · Engineering · #Advanced Mathematical Modeling in Engineering #Composite Material Mechanics #Advanced Numerical Methods in Computational Mathematics

paper · pdf · doi:10.48550/arxiv.2001.06317

Abstract

This paper was devoted to study the quantitative homogenization problems for nonlinear elliptic operators in perforated domains. We obtained a sharp error estimate O(ε) when the problem was anchored in the reference domain εω. If concerning a bounded perforated domain, one will see a bad influence from the boundary layers, which leads to the loss of the convergence rate by O(ε^1/2). Equipped with the error estimates, we developed both interior and boundary Lipschitz estimates at large-scales. As an application, we received the so-called quenched Calderón-Zygumund estimates by Shen's real arguments. To overcome some difficulties, we improved the extension theory from (\cite[Theorem 4.3]OSY) to L^p-versions with (2d)/(d+1)-ε

Citations

• Higher-order pathwise theory of fluctuations in stochastic\n homogenization

Cited by

• suboptimal error estimates for homogenization of linear elasticity systems on perforated domains
• Weighted Meyers estimates in perforated domains

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