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Schwarz boundary value problem on a triangle. (English) Zbl 1474.35215

Summary: 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 parqueting-reflection 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.

MSC:

35F15 Boundary value problems for linear first-order PDEs
35C15 Integral representations of solutions to PDEs
30E25 Boundary value problems in the complex plane
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