Approximate Correctors and Convergence Rates in Almost-Periodic Homogenization

Abstract

We carry out a comprehensive study of quantitative homogenization of second-order elliptic systems with bounded measurable coefficients that are almost-periodic in the sense of H. Weyl. We obtain uniform local $L^2$ estimates for the approximate correctors in terms of a function that quantifies the almost-periodicity of the coefficient matrix. We give a condition that implies the existence of (true) correctors. These estimates as well as similar estimates for the dual approximate correctors yield optimal or near optimal convergence rates in $H^1$ and $L^2$.The $L^2$-based Hölder and Lipschitz estimates at large scale are also established.

Minor revision; 49 pages

References in corpus (3)

• Convergence Rates in Periodic Homogenization of Systems of Elasticity
• Boundary Estimates in Elliptic Homogenization
• On the temporal evolution of spicules observed with IRIS, SDO and Hinode

Cited by in corpus (3)

• Uniform boundary regularity in almost-periodic homogenization
• Convergence rates for general elliptic homogenization problems in a bounded Lipschitz domain
• Optimal Boundary Estimates for Stokes Systems in Homogenization Theory