# Existence, regularity and structure of confined elasticae

created by novaga on 04 Aug 2015
modified by masnou on 27 Jan 2017

[BibTeX]

Accepted Paper

Inserted: 4 aug 2015
Last Updated: 27 jan 2017

Journal: ESAIM: COCV
Year: 2016

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.