Green's matrices of second order elliptic systems with measurable coefficients in two dimensional domains

TL;DR

This paper investigates Green's matrices for second order elliptic systems with measurable coefficients in two-dimensional domains, establishing their existence, uniqueness, and pointwise estimates.

Contribution

It provides new results on the existence, uniqueness, and estimates of Green's matrices for elliptic systems with measurable coefficients in 2D domains.

Findings

Existence of Green's matrices established

Uniqueness of Green's matrices proven

Pointwise estimates derived for Green's matrices

Abstract

We study Green's matrices for divergence form, second order strongly elliptic systems with bounded measurable coefficients in two dimensional domains. We establish existence, uniqueness, and pointwise estimates of the Green's matrices.