复平面上单连通域的传输问题

IF 2.3 2区数学 Q1 MATHEMATICS

Journal of Differential Equations Pub Date : 2025-03-13 DOI:10.1016/j.jde.2025.113216

María J. Carro , Virginia Naibo , María Soria-Carro

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引用次数: 0

摘要

本文首先研究了一个与实线和上下半平面给出的实域上的同胚相关的新问题的可解性结果，研究了具有加权Lebesgue空间数据的平面上单连通域上传输问题的存在唯一性。我们的技术是基于希尔伯特变换的共形映射和Rellich恒等式的使用，并受到先前关于Dirichlet， Neumann和Zaremba问题的工作的启发。

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Transmission problems for simply connected domains in the complex plane

We study existence and uniqueness of a transmission problem in simply connected domains in the plane with data in weighted Lebesgue spaces by first investigating solvability results of a related novel problem associated to a homeomorphism in the real line and domains given by the upper and lower half planes. Our techniques are based on the use of conformal maps and Rellich identities for the Hilbert transform, and are motivated by previous works concerning the Dirichlet, Neumann and Zaremba problems.

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来源期刊

Journal of Differential Equations 数学-数学

CiteScore

4.40

自引率

8.30%

发文量

543

审稿时长

9 months

期刊介绍： The Journal of Differential Equations is concerned with the theory and the application of differential equations. The articles published are addressed not only to mathematicians but also to those engineers, physicists, and other scientists for whom differential equations are valuable research tools. Research Areas Include: • Mathematical control theory • Ordinary differential equations • Partial differential equations • Stochastic differential equations • Topological dynamics • Related topics