Uniqueness and minimality of Euler's elastica with monotone curvature

2024/02/20 by Tatsuya Miura, Miura, Tatsuya, Glen Wheeler +1 · 1 citation
Computer Science · Engineering · #49Q10 and 53A04 #Analysis of PDEs (math.AP) #Contact Mechanics and Variational Inequalities #Differential Geometry (math.DG) #Elasticity and Material Modeling #Elasticity and Wave Propagation #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2402.12771

openalex publication_date 2024/02/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/03

Abstract

For an old problem of Euler's elastica we prove the novel global property that every planar elastica with non-constant monotone curvature is uniquely minimal subject to the clamped boundary condition. We also partly extend this unique minimality to the length-penalised case; this result is new even in view of local minimality. As an application we prove uniqueness of global minimisers in the straightening problem for generic boundary angles.

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