Convergence Rates and Hölder 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 Hölder estimates for the Dirichlet problem in a bounded $C^{1,\alpha }$ domain.

41 pages; minor revision of the previous version

References in corpus (1)

• An optimal error estimate in stochastic homogenization of discrete elliptic equations

Cited by in corpus (1)

• Lipschitz estimates in almost-periodic homogenization