# Existence, regularity and structure of confined elasticae

created by novaga on 04 Aug 2015
modified on 01 Feb 2018

[BibTeX]

Published Paper

Inserted: 4 aug 2015
Last Updated: 1 feb 2018

Journal: ESAIM: COCV
Volume: 24
Number: 1
Pages: 25-43
Year: 2018

Abstract:

We consider the problem of minimizing the bending or elastic energy among Jordan curves confined in a given open set $\Omega$. We prove existence, regularity and some structural properties of minimizers. In particular, when $\Omega$ is convex we show that a minimizer is necessarily a convex curve. We also provide an example of a minimizer with self-intersections.