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

ZHANG Wen-wen, LI Ping-run

doi:10.13371/j.cnki.chin.q.j.m.2024.03.004

Chinese Quarterly Journal of Mathematics >

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

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

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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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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ZHANG Wen-wen, LI Ping-run . On the Method of Solution for the Non-Homogeneous Generalized Riemann-Hilbert Boundary Value Problems[J]. Chinese Quarterly Journal of Mathematics, 2024 , 39(3) : 262 -269 . DOI: 10.13371/j.cnki.chin.q.j.m.2024.03.004

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