解析函数在多连通区域上的间断Riemann-Hilbert问题

北京大学学报（自然科学版）

解析函数在多连通区域上的间断Riemann-Hilbert问题

闻国椿

北京大学数学科学学院, 数学及其应用教育部重点实验室, 北京 100871;

收稿日期:2012-12-07 出版日期:2013-11-20 发布日期:2013-11-20

Discontinuous Riemann-Hilbert Problem for Analytic Functions in Multiply Connected Domains

WEN Guochun

Key Lab of Mathematics and Applied Mathematics, School of Mathematical Sciences, Peking University, Beijing 100871;

Received:2012-12-07 Online:2013-11-20 Published:2013-11-20

摘要/Abstract

摘要： 针对解析函数在多连通区域上的间断边值问题没有得完全的解决, 提出完整解决解析函数在多连通区域上的间断Riemann-Hilbert边值问题的方法, 并给出此间断边值问题的适定提法, 证明了该间断边值问题解的存在唯一性。

关键词: 间断Riemann-Hilbert问题, 解析函数, 多连通区域

Abstract: Though the general discontinuous Riemann-Hilbert problem for analytic functions in simply connected domains was solved, the general discontinuous Riemann-Hilbert problem for analytic functions in multiply connected domains has not been completely solved. The author proposes a well posed-ness of general discontinous Riemann-Hilbert problem for analytic functions, and proves the uniqueness and existence of solutions for the problem.

Key words: discontinuous Riemann-Hilbert problems, analytic functions, multiply connected domains

中图分类号:

O175

闻国椿. 解析函数在多连通区域上的间断Riemann-Hilbert问题[J]. 北京大学学报（自然科学版）.

WEN Guochun. Discontinuous Riemann-Hilbert Problem for Analytic Functions in Multiply Connected Domains[J]. Acta Scientiarum Naturalium Universitatis Pekinensis.

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https://xbna.pku.edu.cn/CN/Y2013/V49/I6/937