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Harmonic functions which vanish on a cylindrical surface
Author(s)
Date Issued
2016-01-15
Date Available
2018-01-15T02:00:10Z
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
Language
English
Status of Item
Peer reviewed
This item is made available under a Creative Commons License
File(s)
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Name
cylinder_extension_6a.pdf
Size
150.58 KB
Format
Adobe PDF
Checksum (MD5)
964289ef8554ec1b4e4ea8ab3fd7afdb
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