Extension results for harmonic functions which vanish on cylindrical surfaces
|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 continuation; Green function; Cylindrical 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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