Approximate correctors and convergence rates in almost-periodic homogenization (Q1689519)

The aim of this study is the quantitative homogenization of second-order elliptic equations with bounded measurable coefficients which are almost-periodic in the sense of Weyl/Besicovitch. The target equation is posed in an ``homogeneous'' domain. Uniform local \(L^2\) estimates for approximate correctors are obtained in terms of a function that quantifies the almost-periodicity of the coefficient matrix. Furthermore, a condition that implies the existence of correctors is given.