Calculus of Variations and Geometric Measure Theory
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C. Mantegazza - M. Pozzetta

The Lojasiewicz-Simon Inequality for the Elastic Flow

created by pozzetta1 on 31 Jul 2020
modified by root on 30 Sep 2020


Submitted Paper

Inserted: 31 jul 2020
Last Updated: 30 sep 2020

Year: 2020


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


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