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arXiv · 1606.04629

Uniform boundary regularity in almost-periodic homogenization

Jinping Zhuge
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Abstract

In the present paper, we generalize the theory of quantitative homogenization for second-order elliptic systems with rapidly oscillating coefficients in $APW^2(\mathbb{R}^d)$, which is the space of almost-periodic functions in the sense of H. Weyl. We obtain the large scale uniform boundary Lipschitz estimate, for both Dirichlet and Neumann problems in $C^{1,\alpha}$ domains. We also obtain large scale uniform boundary H\"{o}lder estimates in $C^{1,\alpha}$ domains and $L^2$ Rellich estimates in Lipschitz domains.

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Jinping Zhuge. 2016-06-15. Uniform boundary regularity in almost-periodic homogenization. https://doi.org/10.1016/j.jde.2016.09.031

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