A reflection result for harmonic functions which vanish on a cylindrical surface

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Title: A reflection result for harmonic functions which vanish on a cylindrical surface
Authors: Gardiner, Stephen J.
Render, Hermann
Permanent link: http://hdl.handle.net/10197/7703
Date: Nov-2016
Abstract: Suppose that a harmonic function h on a finite cylinder U vanishes on the curved part A of the boundary. It was recently shown that h then has a harmonic continuation to the infinite strip bounded by the hyperplanes containing the flat parts of the boundary. This paper examines what can be said if the above function h is merely harmonic near A (and inside U). It is shown that h then has a harmonic extension to a larger domain formed by radial reflection.
Type of material: Journal Article
Publisher: Elsevier
Journal: Journal of Mathematical Analysis and Applications
Volume: 443
Issue: 1
Start page: 81
End page: 91
Copyright (published version): 2016 Elsevier
Keywords: Harmonic continuationGreen functionCylindrical harmonics
DOI: 10.1016/j.jmaa.2016.05.007
Language: en
Status of Item: Peer reviewed
Appears in Collections:Mathematics and Statistics Research Collection

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