# Existence, regularity and structure of confined elasticae.

1 MMCS - Modélisation mathématique, calcul scientifique
ICJ - Institut Camille Jordan [Villeurbanne]
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.
Keywords :
Document type :
Preprints, Working Papers, ...
Domain :

https://hal.archives-ouvertes.fr/hal-01183342
Contributor : François Dayrens <>
Submitted on : Monday, August 24, 2015 - 2:03:46 PM
Last modification on : Monday, May 13, 2019 - 11:11:52 AM
Long-term archiving on : Wednesday, April 26, 2017 - 10:04:49 AM

### Files

Elasticae.pdf
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### Identifiers

• HAL Id : hal-01183342, version 1
• ARXIV : 1508.05785

### Citation

François Dayrens, Simon Masnou, Matteo Novaga. Existence, regularity and structure of confined elasticae.. 2015. ⟨hal-01183342⟩

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