A gradient flow for the p-elastic energy defined on closed planar curves

2018/11/15 by Shinya Okabe, Okabe, Shinya, Paola Pozzi +3 · 1 citation
Computer Science · Mathematics · #35K92 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1811.06608

openalex publication_date 2018/11/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the evolution of closed inextensible planar curves under a second order flow that decreases the p-elastic energy. A short time existence result for p ∈ (1,∞) is obtained via a minimizing movements method. For p = 2, that is in the case of the classic elastic energy, long-time existence is retrieved.

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• Stability of flat-core pinned p-elasticae

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