Schwarz problem in a ring domain*

Abstract

In this article, we discuss the solutions of Schwarz problem in a ring domain. Firstly we introduce the solutions of inhomogeneous Cauchy-Riemann equation. Afterwards we extend the discussions to higher-order equations. The relevant solvability conditions are obtained. The last part is reserved for the solutions of higher-order linear equations in $\mathbb{C}$.

Keywords:

• Schwarz boundary value problem
• ring domain
• singular integral equations
• Fredholm alternative

AMS CLASSIFICATIONS:

• 35J40
• 35C15
• 31A10

Acknowledgments

The authors thank to the referees for their comments and suggestions to improve this article.

Disclosure statement

No potential conflict of interest was reported by the author(s).