On the Solution of a Riemann-Type Boundary-Value Problem for Quasi-Harmonic Functions of the First Kind in Arbitrary Single-Connected Domains

This article considers a Riemann-type boundary value problem for quasiharmonic functions in arbitrary simply-connected domains with smooth boundaries. A special integral representation of analytic functions of a complex variable is constructed, which allows us to develop a constructive method for solving the considered boundary value problem in classes of quasiharmonic functions of the first kind in arbitrary simply-connected domains. It is proven that, depending on the value of the Cauchy index of the boundary condition coefficient, this problem is equivalent to a well-defined Fredholm integral equation of the second kind.