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.
|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||Copyright (published version):||2016 Elsevier||Keywords:||Harmonic continuation;Green function;Cylindrical 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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