Convergence Rates and Hölder Estimates in Almost-Periodic Homogenization of Elliptic Systems

Zhongwei Shen

Published 2014-04-23, updated 2015-06-24Version 2

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 H\"older estimates for the Dirichlet problem in a bounded $C^{1, \alpha}$ domain.