A boundary integral method for the general conjugation problem in multiply connected circle domains

TL;DR

This paper introduces a boundary integral method using the generalized Neumann kernel to solve the general conjugation problem in multiply connected circle domains, providing a new proof of existence and uniqueness.

Contribution

The paper develops a novel boundary integral approach with a new proof for the general conjugation problem in complex analysis.

Findings

The method effectively solves the conjugation problem in multiply connected domains.

The boundary integral equation with the generalized Neumann kernel is uniquely solvable.

An alternative proof confirms the existence and uniqueness of solutions.

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.