Author(s)

F.J. Rizzo, P.A. Martin, L. Pan & D. Zhang

Abstract

Boundary value problems for linear elliptic partial differential equations may be solved by constructing an exact Green's function for the domain involved. Alternatively, an integral equation defined on the boundary of the domain, with unprescribed boundary data as an unknown, may be solved. It is easily argued that both approaches must be equivalent in the broadest sense. In this paper, the precise equivalence between an exact Green's function and the solution of the boundary integral equation is made explicit. Introduction It is well known, e.g. Kellogg [1], Webster [2], that an exact Green's function G* exists and may be used, in principle, to construct the solution of a boundary value problem governed by a li

Keywords