Willmore-Helfrich L²-flow of curves with natural boundary conditions

2012/11/05 by Dall'Acqua, Anna, Pozzi, Paola · 2 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1211.0949

Abstract

We consider regular open curves in Rⁿ with fixed boundary points and moving according to the L²-gradient flow for a generalisation of the Helfrich functional. Natural boundary conditions are imposed along the evolution. More precisely, at the boundary the curvature vector is equal to the normal projection of a fixed given vector. A long-time existence result together with subconvergence to critical points is proven.

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