NDLI: Harmonic functions which vanish on a cylindrical surface

Content Provider	Semantic Scholar
Author	Gardiner, Stephen J. Render, Hermann
Copyright Year	2016
Abstract	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.
Starting Page	1870
Ending Page	1882
Page Count	13
File Format	PDF HTM / HTML
DOI	10.1016/j.jmaa.2015.08.077
Alternate Webpage(s)	https://researchrepository.ucd.ie/bitstream/10197/7132/1/cylinder_extension_6a.pdf
Alternate Webpage(s)	https://researchrepository.ucd.ie/bitstream/10197/7703/1/cylinder_reflection1a.pdf
Alternate Webpage(s)	https://researchrepository.ucd.ie/rest/bitstreams/19993/retrieve
Alternate Webpage(s)	https://doi.org/10.1016/j.jmaa.2015.08.077
Volume Number	433
Language	English
Access Restriction	Open
Content Type	Text
Resource Type	Article

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