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arXiv · 1604.07559

The {\L}ojasiewicz-Simon gradient inequality for open elastic curves

Anna Dall'Acqua·Paola Pozzi·Adrian Spener
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Abstract

In this paper we consider the elastic energy for open curves in Euclidean space subject to clamped boundary conditions and obtain the \L ojasiewicz-Simon gradient inequality for this energy functional. Thanks to this inequality we can prove that a (suitably reparametrized) solution to the associated $L^2$-gradient flow converges for large time to an elastica, that is to a critical point of the functional.

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Anna Dall'Acqua, Paola Pozzi, Adrian Spener. 2016-04-26. The {\L}ojasiewicz-Simon gradient inequality for open elastic curves. https://doi.org/10.1016/j.jde.2016.04.027

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