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Papers published in the English version of the journal

Schwarz boundary value problem for the polyanalytic equation in the partial eclipse domain

A. Darya, N. Taghizadeh

Faculty of Mathematical Sciences, University of Guilan, 19141, Rasht, Iran

Abstract: In this paper, we consider the Schwarz boundary value problem in the partial eclipse domain. The parqueting–reflection method can be used to construct explicit solutions of complex boundary value problems for partial differential equations. We apply the parqueting–reflection principle for the partial eclipse domain to achieve the points of the complex plane. Then, using this method, we introduce the poly-Schwarz operator and the T-type operator for the partial eclipse domain and study the properties of these operators. Finally, based on the properties of the poly-Schwarz operator and the T-type operator, we investigate the schwarz problem for the inhomogeneous polyanalytic equation in the partial eclipse domain and provide an explicit solution.

Key words: Schwarz boundary value problem, parqueting–reflection method, polyanalytic equation, the partial eclipse domain.

Received: 09.01.2025
Revised: 08.04.2025
Accepted: 22.05.2025

Language: English

 English version: Computational Mathematics and Mathematical Physics, 2025, 65:8, 1815–1822