#### Vol. 8, No. 7, 2015

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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
##### 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 ${C}^{1,\alpha }$ domain.

##### Keywords
homogenization, almost periodic coefficients, approximate correctors, convergence rates
##### Mathematical Subject Classification 2010
Primary: 35B27, 35J55
##### Milestones
Accepted: 24 June 2015
Published: 18 September 2015
##### Authors
 Zhongwei Shen Department of Mathematics University of Kentucky Lexington, KY 40506 United States