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Evolution of open elastic curves in ℝn subject to fixed length and natural boundary conditions
-
Anna Dall'Acqua
,
Chun-Chi Lin
Published/Copyright:
May 28, 2014
Abstract
We consider regular open curves in ℝn with fixed boundary points, curvature equal to zero at the boundary, subject to a fixed length constraint and moving according to the L2-gradient flow of the elastic energy. For this flow we prove a long-time existence result and subconvergence to critical points.
Keywords: Geometric evolution equation; fourth order problem; natural boundary conditions; elastic energy; Willmore functional
Received: 2013-11-11
Accepted: 2014-2-10
Published Online: 2014-5-28
Published in Print: 2014-6-28
©2014 Walter de Gruyter Berlin/Boston
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Keywords for this article
Geometric evolution equation;
fourth order problem;
natural boundary conditions;
elastic energy;
Willmore functional
Articles in the same Issue
- Frontmatter
- Pseudo-orthants as a generalisation of orthants
- Uniqueness of meromorphic functions sharing three sets – Further study
- Radius problems associated with pre-Schwarzian and Schwarzian derivatives
- Entire functions sharing certain values with their derivatives
- Alternative proofs of a formula for Bernoulli numbers in terms of Stirling numbers
- Local separability property for Reifenberg sets in parabolic space
- Sharp inequalities for the psi function and harmonic numbers
- Evolution of open elastic curves in ℝn subject to fixed length and natural boundary conditions
- Refinements of the Ostrowski inequality in terms of the cumulative variation and applications
- Erratum to Analysis 34(1), pg. 81–109
- 10.1515/anly-2014-0002
