Convergence rates and Hölder estimates in almost-periodic homogenization of elliptic systems

Shen, Zhongwei

doi:10.2140/apde.2015.8.1565

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Convergence rates and Hölder estimates in almost-periodic homogenization of elliptic systems

Zhongwei Shen

Vol. 8 (2015), No. 7, 1565–1601

DOI: 10.2140/apde.2015.8.1565

Abstract

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 $C^{1, α}$ domain.

Keywords

homogenization, almost periodic coefficients, approximate correctors, convergence rates

Mathematical Subject Classification 2010

Primary: 35B27, 35J55

Milestones

Received: 24 April 2014

Accepted: 24 June 2015

Published: 18 September 2015

Authors

Zhongwei Shen
Department of Mathematics University of Kentucky Lexington, KY 40506 United States

Vol. 8, No. 7, 2015