The Schwarz boundary value problem for boundary values in the sense of distributions

TL;DR

This paper develops solutions to the Schwarz boundary value problem for the unit disk and upper half-plane when boundary conditions are specified as distributions, extending classical boundary value problem methods.

Contribution

It introduces a method to solve the Schwarz boundary value problem with boundary conditions in the sense of distributions, broadening the scope of classical solutions.

Findings

Constructed solutions for the Schwarz boundary value problem with distributional boundary conditions.

Extended classical boundary value problem techniques to distributional boundary data.

Provided a framework applicable to complex analysis and PDEs with generalized boundary conditions.

Abstract

We construct solutions to the Schwarz boundary value problem on the unit disk and the upper half-plane when the boundary condition is with respect to boundary values in the sense of distributions.