Three boundary value problems of the Cauchy-Riemann equation in the Eclipse domain

被引：3

作者：

Emkanpour, Hamed ^{[1
]}

Taghizadeh, Nasir ^{[1
]}

机构：

[1] Univ Guilan, Fac Math Sci, Rasht, Iran

来源：

COMPLEX VARIABLES AND ELLIPTIC EQUATIONS | 2024年 / 69卷 / 03期

关键词：

Complex plane; parqueting-reflection technique; boundary value problems; Cauchy-Riemann equation; Cauchy-Pompeiu formula; Poisson kernel; Schwarz; Dirichlet; Neumann; Eclipse; SCHWARZ PROBLEM; LENS;

D O I：

10.1080/17476933.2022.2151004

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this article, by the parqueting-reflection technique, we obtain a covering of the complex plane from reflecting the Eclipse domain. Then, by the Cauchy-Pompeiu formula, we derive the generalized Cauchy-Pompeiu representation formula in the Eclipse domain. In addition, we consider the Schwarz boundary value problem (BVP) for the nonhomogeneous Cauchy-Riemann equation and the explicit expressions of solution and the condition of solvability. Besides, by using the Schwarz BVP, we investigate the inhomogeneous Dirichlet and homogeneous Neumann BVPs.

引用

页码：510 / 529

页数：20

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