Chinese Quarterly Journal of Mathematics ›› 2024, Vol. 39 ›› Issue (3): 262-269.doi: 10.13371/j.cnki.chin.q.j.m.2024.03.004

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

  

  1. School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China
  • Received:2023-11-14 Online:2024-09-30 Published:2024-09-30
  • Contact: 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; E-mail:z6483384940224@163.com
  • About author: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.
  • Supported by:
    Supported by National Natural Science Foundation of China (Grant No. 11971015).

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

CLC Number: