ABSTRACT
Green’s functions are useful in solving Dirichlet problems of potential theory in itself and, in the case of conformal mapping, of a region onto a circular disk. In the latter case a relationship is needed between conformal mapping and Green’s function for the circle. Although no unique expression is available for Green’s function for a circle, yet an integral representation of Green’s function for the disk leads to the Poisson integral representation. Besides certain Green’s functions determined for Laplace’s equation in a circle, semi-circle, and a sector which have been discussed in Chapter 8, there are other results for Green’s function for a circle, which are presented in this chapter. Green’s functions for the ellipse, certain half-plane regions and the parallel strip are determined, and an interpolation method for computation of Green’s functions for convex regions is presented.
