The Schwarz problem in multiply connected domains and the Schottky-Klein prime function

被引：27

作者：

Crowdy, Darren ^{[1
]}

机构：

[1] Univ London Imperial Coll Sci Technol & Med, Dept Math, London SW7 2AZ, England

来源：

COMPLEX VARIABLES AND ELLIPTIC EQUATIONS | 2008年 / 53卷 / 03期

基金：

英国工程与自然科学研究理事会;

关键词：

Schwarz problem; Schottky-Klein prime function; Multiply connected;

D O I：

10.1080/17476930701682897

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This article presents concise integral formulae for the solution of the Schwarz problem (and modified Schwarz problem) in multiply connected circular planar domains. The form of the solution is novel in that the kernels appearing in the integral formula are expressed in terms of the Schottky-Klein prime function on the Schottky double of the multiply connected domain. The well-known Poisson integral formula and Villat formula are retrieved as special cases.

引用

页码：221 / 236

页数：16

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