The Green function estimates for strongly elliptic systems of second order

Abstract

We establish existence and pointwise estimates of fundamental solutions and Green's matrices for divergence form, second order strongly elliptic systems in a domain $\Omega \subseteq \mathbb{R}^n$, $n \geq 3$, under the assumption that solutions of the system satisfy De Giorgi-Nash type local H\"{o}lder continuity estimates. In particular, our results apply to perturbations of diagonal systems, and thus especially to complex perturbations of a single real equation.