Decomposition and pointwise estimates of periodic Green functions of some elliptic equations with periodic oscillatory coefficients
Marc Josien · Asymptotic Analysis · 2019
This article is about the [Formula: see text]-periodic Green function [Formula: see text] of the multiscale elliptic operator [Formula: see text], where [Formula: see text] is a [Formula: see text]-periodic, coercive, and Hölder continuous matrix, and n is a large integer. We prove here pointwise estimates on [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] in dimensions [Formula: see text]. Moreover, we derive an explicit decomposition of this Green function, which is of independent interest. These results also apply for systems.