A Riemann-Hilbert boundary value problem in a bounded sector

被引：5

作者：

Akel, Mohamed S. ^{[1
,2
]}

Alabbad, F. ^{[1
]}

机构：

[1] King Faisal Univ, Dept Math, Fac Sci, Al Ahsaa 31982, Saudi Arabia

[2] South Valley Univ, Dept Math, Fac Sci, Qena 83523, Egypt

来源：

COMPLEX VARIABLES AND ELLIPTIC EQUATIONS | 2015年 / 60卷 / 04期

关键词：

45E05; 30G20; 30E25; Schwarz-type integral; Riemann-Hilbert problem; boundary value problems; Pompeiu-type integral; Cauchy-Riemann equation; DIRICHLET PROBLEM; GREEN-FUNCTIONS; EQUATION;

D O I：

10.1080/17476933.2014.944866

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this article a Riemann-Hilbert boundary value problem in a bounded sector domain with angle is considered. A plane parqueting-reflection technique is used. Boundary behaviours of resulting integral operators are discussed in detail. Then we study the Riemann-Hilbert boundary value problem, with an arbitrary index, for both homogeneous and inhomogeneous Cauchy-Riemann equations. Expressions of solutions and the condition of solvability are explicitly obtained.

引用

页码：493 / 509

页数：17

共 31 条

[1]

Abdymanapov SA., 2005, Eurasian Math J, V3, P22

[2] Two basic boundary-value problems for the inhomogeneous Cauchy-Riemann equation in an infinite sector [J].