Structure and classification results for the ∞-elastica problem

IF 1.7 1区数学 Q1 MATHEMATICS

American Journal of Mathematics Pub Date : 2019-08-05 DOI:10.1353/ajm.2022.0030

R. Moser

引用次数: 6

Abstract

abstract:We consider the following variational problem: among all curves in $\Bbb{R}^n$ 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.

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∞弹性问题的结构与分类结果

文摘：我们考虑以下变分问题：在$\Bbb｛R｝^n$中所有具有指定端点和端点处指定切线的固定长度的曲线中，最小化曲率的$L^\infty$范数。我们证明了这个问题的解，以及广义版本的解，都是以微分方程组为特征的。此外，我们有很多关于解决方案结构的信息，这允许进行分类。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

American Journal of Mathematics 数学-数学

CiteScore

3.20

自引率

0.00%

发文量

审稿时长

24 months

期刊介绍： The oldest mathematics journal in the Western Hemisphere in continuous publication, the American Journal of Mathematics ranks as one of the most respected and celebrated journals in its field. Published since 1878, the Journal has earned its reputation by presenting pioneering mathematical papers. It does not specialize, but instead publishes articles of broad appeal covering the major areas of contemporary mathematics. The American Journal of Mathematics is used as a basic reference work in academic libraries, both in the United States and abroad.