The second-order L2-flow of inextensible elastic curves with hinged ends in the plane

Chun-Chi Lin, Yang-Kai Lue, Hartmut R. Schwetlick

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4 Citations (Scopus)


In this article, we study the evolution of open inextensible planar curves with hinged ends. We obtain long time existence of C-smooth solutions during the evolution, given the initial curves that are only C2-smooth with vanishing curvature at the boundary. Moreover, the asymptotic limits of this flow are inextensible elasticae. Our method and result extend the work by Wen (Duke Math. J. 70(3):683–698, 1993).

Original languageEnglish
Pages (from-to)263-291
Number of pages29
JournalJournal of Elasticity
Issue number1
Early online date12 Feb 2015
Publication statusPublished - Apr 2015


  • Elastic energy
  • Geometric flow
  • Hinged boundary conditions
  • Second-order parabolic equation
  • Willmore functional

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