Homogenization of Elliptic Differential Equations in One-Dimensional Spaces

Abstract

Linear elliptic differential equations with periodic coefficients in one-dimensional domains are considered. The approximation properties of the homogenized system are investigated. For $H^{-1}$-data, it turns out that the order of approximation is strongly related to the decay of the Fourier coefficients of the $L^2$-functions involved.