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Short time existence for the elastic flow of clamped curves
Author(s) -
Spener Adrian
Publication year - 2017
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201600304
Subject(s) - mathematics , mathematical analysis , flow (mathematics) , contraction (grammar) , dependency (uml) , property (philosophy) , geometry , medicine , philosophy , systems engineering , epistemology , engineering
We show well‐posedness of the elastic flow of open curves with clamped boundary conditions. To show short time existence we prove that the linearised problem has the property of maximal L p ‐regularity and use the contraction principle to obtain the solution. Moreover, we show analyticity of the solution and its analytic dependency on the initial curve. With the developed methods we also prove long time existence of the flow if the initial curve is close to an elastica.