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Title
On the analyticity of critical points of the Möbius energy
AuthorBlatt, Simon ; Vorderobermeier, Nicole
Published in
Calculus of Variations and Partial Differential Equations, Berlin, 2019, Vol. 58, Issue 16, page 1-28
PublishedBerlin : Springer Berlin Heidelberg, 2019
LanguageGerman
Document typeJournal Article
ISSN1432-0835
URNurn:nbn:at:at-ubs:3-11006 Persistent Identifier (URN)
DOI10.1007/s00526-018-1443-6 
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 The work is publicly available
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On the analyticity of critical points of the Möbius energy [0.57 mb]
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Abstract (English)

We prove that smooth critical points of the Möbius energy E parametrized by arc-length are analytic. Together with the main result in Blatt et al. (Trans Am Math Soc 368(9):63916438, 2016) this implies that critical points of the Möbius energy with merely bounded energy are not only C but also analytic. Our proof is based on Cauchys method of majorants and a decomposition of the gradient which has already proved useful in the proof of the regularity results in Blatt and Reiter (Manuscr Math 140(12):2950, 2013) and Blatt et al. (Trans Am Math Soc 368(9):63916438, 2016). To the best of the authors knowledge, this is the first analyticity result in the context of non-local differential equations.

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CC-BY-License (4.0)Creative Commons Attribution 4.0 International License