Explicit solution of a class of Riemann-Hilbert problems

Abstract

Analytical solutions to a special class of Riemann-Hilbert boundary value problems on multiply connected domains are presented. The solutions are expressed, up to a finite number of accessory parameters, as non-singular indefinite integrals whose integrands are expressed in terms of the Schottky-Klein prime function associated with the Schottky double of the planar domain.