Uniform boundary regularity in almost-periodic homogenization

Abstract

In the present paper, we generalize the theory of quantitative homogenization for second-order elliptic systems with rapidly oscillating coefficients in $AP{W}^2({\mathbb{R}}^d)$, 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 Hölder estimates in $C^{1,\alpha }$ domains and $L^2$ Rellich estimates in Lipschitz domains.

29 pages

References in corpus (8)

• Lipschitz regularity for elliptic equations with random coefficients
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Cited by in corpus (4)

• Convergence Rates in Almost-Periodic Homogenization of Higher-order Elliptic Systems
• Optimal Boundary Estimates for Stokes Systems in Homogenization Theory
• Uniform Boundary Estimates in Homogenization of Higher Order Elliptic Systems
• Regularity theory of elliptic systems in $\epsilon$-scale flat domains