Fundamental Solutions for Second Order Linear Elliptic Partial Differential Equations

Abstract

This paper is concerned with outlining some fundamental solutions and Green's functions for a system of second order linear elliptic partial differential equations in two independent variables. The fundamental solution and a number of Green's functions are given in relatively, elementary closed form for some cases when the coefficients in the equations are constant. When the coefficients are variable the fundamental solution is obtained for some particular classes of equations.