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<p>In this paper, we investigate boundary value problems for the Cauchy-Riemann equations on a novel domain called the partial eclipse domain in the complex plane. The study extends classical methods of solving Dirichlet and Schwarz boundary value problems by employing the parqueting-reflection principle. This principle allows us to construct an integral representation formulas that are crucial for obtaining explicit solutions. Specifically, we present solutions for inhomogeneous Dirichlet boundary value problems, as well as solutions for the Schwarz boundary value problem, for the Bitsadze equations on the partial eclipse domain. We provide necessary and sufficient conditions for the solvability of these problems.</p>

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THE DIRICHLET AND SCHWARZ PROBLEMS FOR THE BITSADZE EQUATION IN A PARTIAL ECLIPSE DOMAIN

  • 期刊论文

  • 发表日期：

    2026年3月31日

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  • B. Karaca

摘要

In this paper, we investigate boundary value problems for the Cauchy-Riemann equations on a novel domain called the partial eclipse domain in the complex plane. The study extends classical methods of solving Dirichlet and Schwarz boundary value problems by employing the parqueting-reflection principle. This principle allows us to construct an integral representation formulas that are crucial for obtaining explicit solutions. Specifically, we present solutions for inhomogeneous Dirichlet boundary value problems, as well as solutions for the Schwarz boundary value problem, for the Bitsadze equations on the partial eclipse domain. We provide necessary and sufficient conditions for the solvability of these problems.