Approximate Correctors and Convergence Rates in Almost-Periodic Homogenization

2016/03/10 by Shen, Zhongwei, Zhuge, Jinping · 1 citation
#35B27 #74Q20 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1603.03139

Abstract

We carry out a comprehensive study of quantitative homogenization of second-order elliptic systems with bounded measurable coefficients that are almost-periodic in the sense of H. Weyl. We obtain uniform local L² estimates for the approximate correctors in terms of a function that quantifies the almost-periodicity of the coefficient matrix. We give a condition that implies the existence of (true) correctors. These estimates as well as similar estimates for the dual approximate correctors yield optimal or near optimal convergence rates in H¹ and L².The L²-based Hölder and Lipschitz estimates at large scale are also established.

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• Optimal convergence rates in multiscale elliptic homogenization

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