The Robin function and conformal welding – A new proof of the existence-Reference-Cited by-同舟云学术

The Robin function and conformal welding – A new proof of the existence

Published:2020-03-01 Issue:1 Volume:27 Page:43-51
ISSN:1072-947X
Container-title:Georgian Mathematical Journal
language:
Short-container-title:

Author:

Dittmar Bodo¹

Affiliation:

1. Institute of Mathematics, Martin-Luther-University, Halle–Wittenberg, 06099Halle (Saale), Germany

Abstract

AbstractGreen’s function of the mixed boundary value problem for harmonic functions is sometimes named the Robin function

{R(z,\zeta\/)}

after the French mathematical physicist Gustave Robin (1855–1897). The aim of this paper is to provide a new proof of the existence of the Robin function for planar n-fold connected domains using a special version of the well-known Koebe’s uniformization theorem and a conformal mapping which is closely related to the Robin function in the simply connected case.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/downloadpdf/journals/gmj/27/1/article-p43.xml

Reference78 articles.

1. Robin’s modulus in a Hele–Shaw problem;Complex Var. Theory Appl.,2004

2. Some harmonic Robin functions in the complex plane;Adv. Pure Appl. Math.,2010

3. Robin functions and energy functionals of multiply connected domains;Pacific J. Math.,1991

4. Robin functions and distortion theorems for regular mappings;Math. Nachr.,2010

Cited by 2 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Inner Dirichlet Problem for the Axial-symmetric Potential;Monogenic Functions in Spaces with Commutative Multiplication and Applications;2023

2. Integral representations in the complex plane and iterated boundary value problems;Rocky Mountain Journal of Mathematics;2022-04-01