Structure and classification results for the $\infty$-elastica problem

Abstract

Consider the following variational problem: among all curves in ${\mathbb{R}}^n$ of fixed length with prescribed end points and prescribed tangents at the end points, minimise the $L^{\infty }$-norm of the curvature. We show that the solutions of this problem, and of a generalised version, are characterised by a system of differential equations. Furthermore, we have a lot of information about the structure of solutions, which allows a classification.

Cited by in corpus (3)

• Variational problems in $L^{\infty }$ involving semilinear second order differential operators
• Complete classification of planar p-elasticae
• Regularity and structure of non-planar $p$-elasticae