SCHWARZ BOUNDARY VALUE PROBLEM ON A TRIANGLE

Document Type: Research articles

Authors

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

2 University of Guilan

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