Riemann-Hilbert boundary value problems in bounded domains in the complex plane

Abstract

This dissertation is devoted to the investigation of some boundary value problems, Riemann-Hilbert-type problem, for complex partial differential systems of the first order in a circular sector, an isosceles orthogonal triangles and a half hexagon. The method of plane parqueting-reflection is used among the main tools to obtain the Schwarz-Poisson-type representation formula for each of these domains. Both the homogeneous and the inhomogeneous Cauchy-Riemann equations, as model first order PDEs