We define the elastic energy of smooth immersed closed curves in 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 Łojasiewicz–Simon inequality, which is at the core of the proof, in a quite concise and versatile way.
The Lojasiewicz-Simon inequality for the elastic flow
Carlo Mantegazza;Marco Pozzetta
2021-01-01
Abstract
We define the elastic energy of smooth immersed closed curves in 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 Łojasiewicz–Simon inequality, which is at the core of the proof, in a quite concise and versatile way.File in questo prodotto:
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