Extension results for harmonic functions which vanish on cylindrical surfaces

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Title: Extension results for harmonic functions which vanish on cylindrical surfaces
Authors: Gardiner, Stephen J.Render, Hermann
Permanent link: http://hdl.handle.net/10197/10812
Date: Jun-2018
Online since: 2019-07-01T09:46:01Z
Abstract: The Schwarz reflection principle applies to a harmonic function which continuously vanishes on a relatively open subset of a planar or spherical boundary surface. It yields a harmonic extension to a predefined larger domain and provides a simple formula for this extension. Although such a point-to-point reflection law is unavailable for other types of surface in higher dimensions, it is natural to investigate whether similar harmonic extension results still hold. This article describes recent progress on such results for the particular case of cylindrical surfaces, and concludes with several open questions.
Type of material: Journal Article
Publisher: Springer
Journal: Analysis and Mathematical Physics
Volume: 8
Issue: 2
Start page: 213
End page: 220
Copyright (published version): 2018 Springer
Keywords: Harmonic continuationGreen functionCylindrical harmonics
DOI: 10.1007/s13324-018-0213-0
Language: en
Status of Item: Peer reviewed
Appears in Collections:Mathematics and Statistics Research Collection

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