Riemann-Hilbert problem for the Cauchy-Riemann operator in lens and lune

被引：4

作者：

Akel, M. ^{[1
,2
]}

机构：

[1] King Faisal Univ, Coll Sci, Math & Stat Dept, Al Ahsaa, Saudi Arabia

[2] South Valley Univ, Dept Math, Fac Sci, Qena, Egypt

来源：

COMPLEX VARIABLES AND ELLIPTIC EQUATIONS | 2017年 / 62卷 / 10期

关键词：

Riemann-Hilbert problem; Cauchy-Riemann equation; Pompeiu-type integral; Schwarz-type integral; BOUNDARY-VALUE-PROBLEMS; GREEN-FUNCTIONS; DIRICHLET PROBLEM; SCHWARZ PROBLEM; EQUATION; REFLECTIONS;

D O I：

10.1080/17476933.2016.1244189

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This article is devoted to study the solvability of the Riemann-Hilbert problem, with arbitrary index, for the Cauchy-Riemann operator in a lens and two complementary lunes. We generalize the corresponding results obtained by Begehr and Vaitekhovich (Complex Var Elliptic Eqs. 2014; 59: 76-84). The parqueting-reflection technique is used. The boundary behaviour of related integral operators of Schwarz type and Pompeiu type is discussed. Then the expressions of the solutions are explicitly obtained.

引用

页码：1570 / 1588

页数：19

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