A Riemann–Hilbert boundary value problem in a triangle

Abstract

In this article a Riemann–Hilbert boundary value problem on an isosceles orthogonal triangle is considered. Using explicit Schwarz–Poisson-type formulae for the triangle, Schwarz-type and Pompeiu-type operators are obtained. Boundary behaviors of these operators are discussed in detail. Finally, we investigate the Riemann–Hilbert boundary value problem for both homogeneous and inhomogeneous Cauchy–Riemann equations. An explicit solvability of the problem is obtained.