Schwarz boundary value problems for polyanalytic equation in a sector ring
Complex Variables
2022-02-01 v1
Abstract
In this article,we first give a modified Schwarz-Pompeiu formula in a general sector ring by proper conformal mappings, and obtain the solution of the Schwarz problem for the Cauchy-Riemann equation in explicit forms. Furthermore, a class of integral operators is introduced together with their properties. Finally, by virtue of these operators, Schwarz problems for a inhomogeneous polyanalytic equation and for a generalized polyanalytic equation are investigated, respectively.
Keywords
Cite
@article{arxiv.2201.12623,
title = {Schwarz boundary value problems for polyanalytic equation in a sector ring},
author = {Zhihua Du and Ying Wang and Min Ku},
journal= {arXiv preprint arXiv:2201.12623},
year = {2022}
}