Document Type : Research Articles

Authors

• Fatemeh Joveini
• Mozhgan Akbari

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

• Schwarz problem
• Cauchy-Pompeiu formula
• Cauchy-Schwarz represen- tation
• Triangle