English

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}
}
R2 v1 2026-06-24T09:08:48.601Z