An integral equation for conformal mapping of triply connected regions onto a disk with circular slits

Abstract

This paper presents an integral equation m ethod for com puting the confor mal m apping function of triply connected regions onto a disk of unit radius with two c oncen tric circu lar slits of rad ii μ ) ( z f 1 < 1 and μ 2 < 1. By using the boundary re lationship satisfied by the mapping function, a related system of nonlinear integral equations via Neum ann kernel is constructed involving the unknown μ 1 and μ 2 . Together with som e norm alizing conditions, a unique solution to the system is then com puted using an optim ization method. Num erical implem entation on some test regions will also be presented.