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Abstract <p> In this paper, we consider the Schwarz boundary value problem for a higher-order complexpartial differential equation in a particular circular lens and two related complementary lunes.First, by applying the parqueting-reflection principle, we obtain a covering for the complex plane.Based on the points derived through this principle, we introduce the T-type and poly-Schwarzoperators and study their properties. In particular, we discuss the boundary behavior of theseoperators. Finally, using the properties of the T-type and poly-Schwarz operators, we investigatethe Schwarz problem for the inhomogeneous generalized Cauchy–Riemann equation in the lensdomain and provide an explicit solution.</p>

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On the Boundary Value Problem for a Generalized Cauchy–Riemann Equation in Lens and Lune

  • 期刊论文

  • 发表日期：

    2025年10月1日

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  • A. Darya,
  • N. Taghizadeh

摘要

Abstract

In this paper, we consider the Schwarz boundary value problem for a higher-order complexpartial differential equation in a particular circular lens and two related complementary lunes.First, by applying the parqueting-reflection principle, we obtain a covering for the complex plane.Based on the points derived through this principle, we introduce the T-type and poly-Schwarzoperators and study their properties. In particular, we discuss the boundary behavior of theseoperators. Finally, using the properties of the T-type and poly-Schwarz operators, we investigatethe Schwarz problem for the inhomogeneous generalized Cauchy–Riemann equation in the lensdomain and provide an explicit solution.