Schwarz boundary problem on a triangle

Document Type : Research Articles

Authors

Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran

Abstract

In this paper, the Schwarz boundary value problem (BVP) for the inhomogeneous Cauchy-Riemann equation in a triangle is investigated explicitly. Firstly, by the technique of parquetingreflection and the Cauchy-Pompeiu representation formula a modified Cauchy-Schwarz representation formula is obtained. Then, the solution of the Schwarz BVP is explicitly solved. In particular, the boundary behaviors at the corner points are considered.

Keywords

Caspian Journal of Mathematical Sciences
Volume 9, Issue 2 - Serial Number 2
September 2020
Pages 266-283

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