数学季刊 >

2024 , Vol. 39 >Issue 3: 262 - 269

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2024.03.004

非齐次Riemann-Hilbert边值问题的求解

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  • School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China
ZHANG Wen-wen (2000-), female, native of Weifang, Shandong, graduate student of Qufu Normal University, under postgraduate, engages in the boundary value problem of analytic function and singular integral equation; LI Ping-run (1966-), male, native of Yanzhou, Shandong, professor of Qufu Normal University, Ph.D., engages in the boundary value problem of analytic function, singular integral equation and Clifford analysis.

收稿日期: 2023-11-14

  网络出版日期: 2024-09-30

基金资助

Supported by National Natural Science Foundation of China (Grant No. 11971015).


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On the Method of Solution for the Non-Homogeneous Generalized Riemann-Hilbert Boundary Value Problems

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  • School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China
ZHANG Wen-wen (2000-), female, native of Weifang, Shandong, graduate student of Qufu Normal University, under postgraduate, engages in the boundary value problem of analytic function and singular integral equation; LI Ping-run (1966-), male, native of Yanzhou, Shandong, professor of Qufu Normal University, Ph.D., engages in the boundary value problem of analytic function, singular integral equation and Clifford analysis.

Received date: 2023-11-14

  Online published: 2024-09-30

Supported by

Supported by National Natural Science Foundation of China (Grant No. 11971015).


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摘要

This paper studies the non-homogeneous generalized Riemann-Hilbert (RH) problems involving two unknown functions. Using the uniformization theorem, such problems are transformed into the case of homogeneous type. By the theory of classical boundary value problems, we adopt a novel method to obtain the sectionally analytic solutions of problems in strip domains, and analyze the conditions of solvability and properties of solutions in various domains.

关键词： Generalized Riemann-Hilbert problem; Uniformization theorem; Analytic solution; Sokhotski-Plemelj formula

本文引用格式

张雯雯, 李平润 . 非齐次Riemann-Hilbert边值问题的求解[J]. 数学季刊, 2024 , 39(3) : 262 -269 . DOI: 10.13371/j.cnki.chin.q.j.m.2024.03.004

Abstract

This paper studies the non-homogeneous generalized Riemann-Hilbert (RH) problems involving two unknown functions. Using the uniformization theorem, such problems are transformed into the case of homogeneous type. By the theory of classical boundary value problems, we adopt a novel method to obtain the sectionally analytic solutions of problems in strip domains, and analyze the conditions of solvability and properties of solutions in various domains.

Key words： Generalized Riemann-Hilbert problem; Uniformization theorem; Analytic solution; Sokhotski-Plemelj formula

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