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arXiv · 1603.03139

Approximate Correctors and Convergence Rates in Almost-Periodic Homogenization

Zhongwei Shen·Jinping Zhuge
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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 $L^2$ 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 $H^1$ and $L^2$.The $L^2$-based H\"older and Lipschitz estimates at large scale are also established.

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Zhongwei Shen, Jinping Zhuge. 2016-03-10. Approximate Correctors and Convergence Rates in Almost-Periodic Homogenization. https://arxiv.org/abs/1603.03139

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