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Convergence rates and Hölder estimates in almost-periodic homogenization of elliptic systems. (English) Zbl 1327.35025

Summary: For a family of second-order elliptic systems in divergence form with rapidly oscillating, almost-periodic coefficients, we obtain estimates for approximate correctors in terms of a function that quantifies the almost periodicity of the coefficients. The results are used to investigate the problem of convergence rates. We also establish uniform Hölder estimates for the Dirichlet problem in a bounded \(C^{1, \alpha}\) domain.

MSC:

35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
35J57 Boundary value problems for second-order elliptic systems
35B15 Almost and pseudo-almost periodic solutions to PDEs
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