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