An Integral Equation Method for Conformal Mapping of Doubly Connected Regions

Abstract

Based on a boundary relationship satisfied by a function which is analytic in a doubly connected region bounded by two closed Jordan curves, an integral equation is constructed. Some applications considered are the conformal mappings from a doubly connected region bounded by two closed smooth Jordan curves onto: (a) an annulus, and (b) a unit disk. Among the kernels involved are the Kerzman-Stein and the Neumann kernels. Keywords: Conformal mapping; Integral equation; Doubly connected region; Kerzman-Stein kernel; Neumann kernel. Berdasarkan kepada hubungan sempadan yang ditepati oleh satu fungsi yang analisis dalam rantau terkait ganda dua yang dibatasi antara dua lengkung Jordan, sebuah persamaan kamiran dibina. Beberapa penggunaannya ialah pemetaan konformal dari rantau terkait ganda dua antara dua lengkung Jordan ke: (a) anulus (b) bulatan unit. Antara inti kamiran yang terlibat ialah inti Kerzman-Stein dan inti Neumann. Katakunci: Pemetaan konformal; Persamaan kamiran; Rantau terkait ganda dua; Inti Kerzman-Stein; Inti Neumann.