# The Lojasiewicz-Simon Inequality for the Elastic Flow

created by pozzetta1 on 31 Jul 2020
modified by root on 04 Aug 2021

[BibTeX]

Accepted Paper

Inserted: 31 jul 2020
Last Updated: 4 aug 2021

Journal: Calc. Var.
Year: 2021
Doi: https://doi.org/10.1007/s00526-020-01916-0

Abstract:

We define the elastic energy of smooth immersed closed curves in $\mathbb{R}^n$ as the sum of the length and the $L^2$–norm of the curvature, with respect to the length measure. We prove that the $L^2$–gradient flow of this energy smoothly converges asymptotically to a critical point. One of our aims was to the present the application of a Lojasiewicz– Simon inequality, which is at the core of the proof, in a quite concise and versatile way