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

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Published/Copyright: February 15, 2018
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Abstract

Green’s function of the mixed boundary value problem for harmonic functions is sometimes named the Robin function R(z,ζ) 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.

Keywords: Robin function
MSC 2010: 35J

Dedicated to Reiner Kühnau on the occasion of his 80th birthday


Acknowledgements

The author wishes to express his thanks to Reiner Kühnau for some hints to the references and Markus Köbis for drawing the figures.

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Received: 2015-04-30
Revised: 2016-05-23
Accepted: 2016-06-22
Published Online: 2018-02-15
Published in Print: 2020-03-01

© 2020 Walter de Gruyter GmbH, Berlin/Boston

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