Seick Kim

The Green function estimates for strongly elliptic systems of second order

We establish existence and pointwise estimates of fundamental solutions and Green’s matrices for divergence form, second order strongly elliptic systems in a domain

L^{2}

\Omega \subseteq {\mathbb{R}}^n, n \geq 3

L^{\infty}

, under the assumption that solutions of the system satisfy De Giorgi-Nash type local Hölder continuity estimates. In particular, our results apply to perturbations of diagonal systems, and thus especially to complex perturbations of a single real equation.

coefficients

We consider divergence form elliptic operators of the form

Gaussian estimates for fundamental solutions to certain parabolic systems

L=-\dv A(x)\nabla

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

, defined in

Global pointwise estimates for Green's matrix of second order elliptic systems

R^{n+1} = \{(x,t)\in R^n \times R \}

Global Estimates for Green’s Matrix of Second Order Parabolic Systems with Application to Elliptic Systems in Two Dimensional Domains

,