A gradient flow for the p-elastic energy defined on closed planar curves

Shinya Okabe; Paola Pozzi; Glen Wheeler

A gradient flow for the p-elastic energy defined on closed planar curves

Differential Geometry 2018-11-19 v1 Analysis of PDEs

Authors: Shinya Okabe , Paola Pozzi , Glen Wheeler

Abstract

We study the evolution of closed inextensible planar curves under a second order flow that decreases the $p$ -elastic energy. A short time existence result for $p \in (1,\infty)$ is obtained via a minimizing movements method. For $p = 2$ , that is in the case of the classic elastic energy, long-time existence is retrieved.

Keywords

p-elastic energy closed planar curves gradient flow minimizing movements short time existence long-time existence inextensible curves

Cite

@article{arxiv.1811.06608,
  title  = {A gradient flow for the p-elastic energy defined on closed planar curves},
  author = {Shinya Okabe and Paola Pozzi and Glen Wheeler},
  journal= {arXiv preprint arXiv:1811.06608},
  year   = {2018}
}

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43 pages

A gradient flow for the p-elastic energy defined on closed planar curves

Abstract

Keywords

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