Harmonic functions which vanish on a cylindrical surface

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Title: Harmonic functions which vanish on a cylindrical surface
Authors: Gardiner, Stephen J.
Render, Hermann
Permanent link: http://hdl.handle.net/10197/7132
Date: 15-Jan-2016
Abstract: Suppose that a harmonic function h on a finite cylinder vanishes on the curved part of the boundary. This paper answers a question of Khavinson by showing that h then has a harmonic continuation to the infinite strip bounded by the hyperplanes containing the flat parts of the boundary. The existence of this extension is established by an analysis of the convergence properties of a double series expansion of the Green function of an infinite cylinder beyond the domain itself.
Type of material: Journal Article
Publisher: Elsevier
Journal: Journal of Mathematical Analysis and Applications
Volume: 433
Issue: 2
Start page: 1870
End page: 1882
Copyright (published version): 2015 Elsevier
Keywords: Harmonic continuationGreen functionCylindrical harmonics
DOI: 10.1016/j.jmaa.2015.08.077
Language: en
Status of Item: Peer reviewed
Appears in Collections:Mathematics and Statistics Research Collection

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