The Łojasiewicz–Simon gradient inequality for open elastic curves

By Anna Dall’Acqua, Paola Pozzi, A. Spener. 2016

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In this paper we consider the elastic energy for open curves in Euclidean space subject to clamped boundary conditions and obtain the Łojasiewicz–Simon gradient inequality for this energy functional. Thanks to this inequality we can prove that a (suitably reparametrized) solution to the associated L2-gradient flow converges for large time to an elastica, that is to a critical point of the functional.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/2d7507908bb9a56af293e17e8efbb6536ccc836e