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Georgian Mathematical Journal

Editor-in-Chief: Kiguradze, Ivan / Buchukuri, T.

Editorial Board: Kvinikadze, M. / Bantsuri, R. / Baues, Hans-Joachim / Besov, O.V. / Bojarski, B. / Duduchava, R. / Engelbert, Hans-Jürgen / Gamkrelidze, R. / Gubeladze, J. / Hirzebruch, F. / Inassaridze, Hvedri / Jibladze, M. / Kadeishvili, T. / Kegel, Otto H. / Kharazishvili, Alexander / Kharibegashvili, S. / Khmaladze, E. / Kiguradze, Tariel / Kokilashvili, V. / Krushkal, S. I. / Kurzweil, J. / Kwapien, S. / Lerche, Hans Rudolf / Mawhin, Jean / Ricci, P.E. / Tarieladze, V. / Triebel, Hans / Vakhania, N. / Zanolin, Fabio


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

Bodo Dittmar
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  • Institute of Mathematics, Martin-Luther-University, Halle–Wittenberg, 06099 Halle (Saale), Germany
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Published Online: 2018-02-15 | DOI: https://doi.org/10.1515/gmj-2017-0057

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

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About the article

Received: 2015-04-30

Revised: 2016-05-23

Accepted: 2016-06-22

Published Online: 2018-02-15


Citation Information: Georgian Mathematical Journal, ISSN (Online) 1572-9176, ISSN (Print) 1072-947X, DOI: https://doi.org/10.1515/gmj-2017-0057.

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