Structure and classification results for the ∞-elastica problem

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Abstract

Consider the following variational problem: among all curves in Rn of fixed length with prescribed end points and prescribed tangents at the end points, minimise the L-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.
Original languageEnglish
Pages (from-to)1299-1329
Number of pages31
JournalAmerican Journal of Mathematics
Volume144
Issue number5
DOIs
Publication statusPublished - 31 Oct 2022

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