Extensions of Harmonic Functions of the Complex Plane Slit Along a Line Segment

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-10-19 DOI:10.1007/s11118-023-10103-7

Armen Grigoryan, Andrzej Michalski, Dariusz Partyka

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引用次数: 0

Abstract

Abstract Let I be a line segment in the complex plane $$\mathbb C$$ C . We describe a method of constructing a bi-Lipschitz sense-preserving mapping of $$\mathbb C$$ C onto itself, which is harmonic in $$\mathbb C\setminus I$$ C \ I and coincides with a given sufficiently regular function $$f:I\rightarrow \mathbb C$$ f : I → C . As a result we show that a quasiconformal self-mapping of $$\mathbb C$$ C which is harmonic in $$\mathbb C\setminus I$$ C \ I does not have to be harmonic in $$\mathbb C$$ C .

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复平面狭缝调和函数沿线段的扩展

设我是复平面$$\mathbb C$$ C上的一条线段。我们描述了一个构造$$\mathbb C$$ C到自身的双lipschitz保感映射的方法，该映射在$$\mathbb C\setminus I$$ C I中是调和的，并且与给定的充分正则函数$$f:I\rightarrow \mathbb C$$ f: I→C重合。结果表明，$$\mathbb C$$ C的拟共形自映射在$$\mathbb C\setminus I$$ C I中是调和的，并不一定在$$\mathbb C$$ C中是调和的。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.