# The Lojasiewicz-Simon inequality for the elastic flow

created by pozzetta1 on 31 Jul 2020

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Submitted Paper

Inserted: 31 jul 2020
Last Updated: 31 jul 2020

Year: 2020

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