Schwarz problem for the inhomogeneous poly-analytic equation in a half-lens

A. Darya^a, K. Ebrahimzadeh^b, N. Darya^c, N. Darya<sup>c

a</sup> Faculty of Mathematical Sciences, University of Guilan, Namjoo st, P.O. Box 19141, Rasht, Iran
^b Department of Education Guilan, Dr Behzad Research Institute Sama Rasht Branch, Islamic Azad University Rasht, Iran
^c Department of Chemistry, University of Guilan, Namjoo st, P.O. Box 19141, Rasht, Iran

Abstract: In this paper, we consider the Schwarz boundary-value problem for the poly-analytic equation in the half-lens domain. First, using the parqueting-reflection principle, we construct the Poly-Schwarz and T-type operators in the half-lens domain, and then we study the properties of these operators. Furthermore, we establish solvability conditions and examine the Schwarz boundary-value problem for the inhomogeneous poly-analytic equation in a half-lens.

Keywords: boundary-value problem, Schwarz problem, poly-analytic equation, half-lens.

UDC: 517.44, 517.95

MSC: 30E25, 31A10, 35C15, 35F15, 35J25, 45E05

Received: 11.08.2025
Revised: 05.10.2205
Accepted: 05.10.2205

Language: English

DOI: 10.15393/j3.art.2025.18950