Schwarz and Dirichlet Problems for (partial derivative)over-bar-Equation in a Triangular Domain

被引：0

作者：

Darya, A. ^{[1
]}

Taghizadeh, N. ^{[2
]}

机构：

[1] Ali Darya Univ Guilan, Rasht 19141, Iran

[2] Nasir Taghizadeh Univ Guilan, Rasht 19141, Iran

来源：

RUSSIAN MATHEMATICS | 2024年 / 68卷 / 11期

关键词：

Schwarz problem; Dirichlet problem; Cauchy-Riemann equation; triangular domain; BOUNDARY-VALUE-PROBLEMS; CAUCHY-RIEMANN EQUATION;

D O I：

10.3103/S1066369X24700853

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we investigate some boundary value problems for the Cauchy-Riemann equations in the triangular domain M. By the parqueting-reflection method, we obtain a covering of the complex plane from reflecting the domain. Then by the Cauchy-Pompeiu formula, we derive the Cauchy-Schwarz representation formula in M. In addition, we consider the Schwarz boundary value problem for the inhomogeneous Cauchy-Riemann equation and the explicit expressions of solution and condition of solvability. Finally, by using the Schwarz boundary value problem, the solution of the Dirichlet boundary value problem is explicitly solved.

引用

页码：9 / 17

页数：9

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