Structure and classification results for the ∞-elastica problem

Roger Moser

doi:10.1353/ajm.2022.0030

Structure and classification results for the ∞-elastica problem

Roger Moser

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

7 Citations (SciVal)

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Abstract

We consider the following variational problem: among all curves in R ⁿ 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 language	English
Pages (from-to)	1299-1329
Number of pages	31
Journal	American Journal of Mathematics
Volume	144
Issue number	5
DOIs	https://doi.org/10.1353/ajm.2022.0030
Publication status	Published - 31 Oct 2022

Bibliographical note

Publisher Copyright:
. © 2022 by Johns Hopkins University Press.

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10.1353/ajm.2022.0030

infinity-elastica-revised.pdf
This article appeared in the American Journal of Mathematics, Volume 144, Issue 5, Year, pages 1299-1329, Copyright © 2022, Johns Hopkins University Press.
Accepted author manuscript, 383 KB

http://arxiv.org/abs/1908.01569

Cite this

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Structure and classification results for the ∞-elastica problem

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Roger Moser

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Structure and classification results for the ∞-elastica problem

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Roger Moser

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