Convergence Rates and H\"older Estimates in Almost-Periodic Homogenization of Elliptic Systems

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