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<p>In this study, we investigate the Schwarz problem for the Beltrami operator in the upper half of the unit disc in the complex plane. We derive the solution to this boundary value problem and establish the necessary conditions for solvability. Furthermore, we extend our analysis to a second-order equation, providing a comprehensive treatment of the Schwarz problem for higher-order cases. The results presented in this paper contribute to the understanding of boundary value problems associated with the Beltrami operator and their generalizations, offering new insights and potential applications in complex analysis and related fields.</p>

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EXTENSIONS OF THE SCHWARZ PROBLEM FOR THE BELTRAMI OPERATOR IN THE HALF UNIT DISC

  • 期刊论文

  • 发表日期：

    2025年4月1日

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  • Bahriye Karaca

摘要

In this study, we investigate the Schwarz problem for the Beltrami operator in the upper half of the unit disc in the complex plane. We derive the solution to this boundary value problem and establish the necessary conditions for solvability. Furthermore, we extend our analysis to a second-order equation, providing a comprehensive treatment of the Schwarz problem for higher-order cases. The results presented in this paper contribute to the understanding of boundary value problems associated with the Beltrami operator and their generalizations, offering new insights and potential applications in complex analysis and related fields.