The Lojasiewicz-Simon gradient inequality for open elastic curves

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:261

Article

Dall'Acqua, Anna¹  Pozzi, Paola²  Spener, Adrian¹ 

[1] Univ Ulm, Helmholtzstr 18, D-89081 Ulm, Germany

[2] Univ Duisburg Essen, Math Carree, Thea Leymann Str 9, D-45127 Essen, Germany

关键词: Lojasiewicz-Simon gradient inequality;    Elastic energy;    Clamped boundary conditions;    Geometric evolution equation;   

DOI  :  10.1016/j.jde.2016.04.027

来源: Elsevier

【 摘 要 】

In this paper we consider the elastic energy for open curves in Euclidean space subject to clamped boundary conditions and obtain the Lojasiewicz-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. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free