A Boundary Integral Method for the General Conjugation Problem in Multiply Connected Circle Domains

Abstract

We present a boundary integral method for solving a certain class of Riemann-Hilbert problems known as the general conjugation problem. The method is based on a uniquely solvable boundary integral equation with the generalized Neumann kernel. We present also an alternative proof for the existence and uniqueness of the solution of the general conjugation problem.Mathematics Subject Classification (2010). Primary 30E25; Secondary 45B05.