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

IF 1 3区数学 Q1 MATHEMATICS

Potential Analysis 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

Potential Analysis 数学-数学

CiteScore

2.20

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： The journal publishes original papers dealing with potential theory and its applications, probability theory, geometry and functional analysis and in particular estimations of the solutions of elliptic and parabolic equations; analysis of semi-groups, resolvent kernels, harmonic spaces and Dirichlet forms; Markov processes, Markov kernels, stochastic differential equations, diffusion processes and Levy processes; analysis of diffusions, heat kernels and resolvent kernels on fractals; infinite dimensional analysis, Gaussian analysis, analysis of infinite particle systems, of interacting particle systems, of Gibbs measures, of path and loop spaces; connections with global geometry, linear and non-linear analysis on Riemannian manifolds, Lie groups, graphs, and other geometric structures; non-linear or semilinear generalizations of elliptic or parabolic equations and operators; harmonic analysis, ergodic theory, dynamical systems; boundary value problems, Martin boundaries, Poisson boundaries, etc.