|Publication ahead of print|
|Published online||28 September 2017|
Existence, regularity and structure of confined elasticae
1 Institut Camille Jordan, Université Lyon 1, 43, Boulevard du 11 novembre 1918, 69622 Villeurbanne cedex, France.
2 Dipartimento di Matematica, Università di Pisa, Largo Bruno Pontecorvo 5, 56127 Pisa, Italy.
Received: 23 June 2016
Revised: 15 October 2016
Accepted: 17 November 2016
We consider the problem of minimizing the bending or elastic energy among Jordan curves confined in a given open set Ω. We prove existence, regularity and some structural properties of minimizers. In particular, when Ω is convex we show that a minimizer is necessarily a convex curve. We also provide an example of a minimizer with self-intersections.
Mathematics Subject Classification: 49J52 / 49N60 / 49Q10 / 53A04
Key words: Minimization / confined curves / elastic energy / bending energy
© EDP Sciences, SMAI 2017
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