The critical points of the elastic energy among curves pinned at endpoints

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Abstract

In this paper we find curves minimizing the elastic energy among curves whose length is fixed and whose ends are pinned. Applying the shooting method, we can identify all critical points explicitly and determine which curve is the global minimizer. As a result we show that the critical points consist of wavelike elasticae and the minimizers do not have any loops or interior inection points.

Original languageEnglish
Pages (from-to)403-423
Number of pages21
JournalDiscrete and Continuous Dynamical Systems- Series A
Volume42
Issue number1
DOIs
Publication statusPublished - Jan 2022
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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