Green's Functions for Mixed Boundary Value Problems in Regions of Irregular Shape

Abstract

A semi-analytic approach is applied to the construction of Green's functions and matrices of Green's type for Laplace and Klein-Gordon equation in two dimensions. Mixed boundary value problems posed on multiply connected regions are considered. Statements of the problems are complicated by intricate geometry of the regions and different types of boundary conditions imposed on different fragments of the boundary. The approach is based on a combination of the Green's function method and the method of functional equations. Kernels of resolving potentials representing the regular components of the Green's functions to be constructed are built with Green's functions obtained for regions of standard shape.