Existence, regularity and structure of confined elasticae

Dayrens, François; Masnou, Simon; Novaga, Matteo

doi:10.1051/cocv/2016073

Dayrens, François ¹ ; Masnou, Simon ¹ ; Novaga, Matteo ²

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.

ESAIM: Control, Optimisation and Calculus of Variations, Tome 24 (2018) no. 1, pp. 25-43.

Résumé

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.

Reçu le : 2016-06-23
Accepté le : 2016-11-17

MR Zbl

DOI : 10.1051/cocv/2016073

Classification : 49J52, 49N60, 49Q10, 53A04
Mots clés : Minimization, confined curves, elastic energy, bending energy

Affiliations des auteurs :

Dayrens, François ¹ ; Masnou, Simon ¹ ; Novaga, Matteo ²

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Dayrens, François; Masnou, Simon; Novaga, Matteo. Existence, regularity and structure of confined elasticae. ESAIM: Control, Optimisation and Calculus of Variations, Tome 24 (2018) no. 1, pp. 25-43. doi : 10.1051/cocv/2016073. http://archive.numdam.org/articles/10.1051/cocv/2016073/

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