Existence, regularity and structure of confined elasticae.

François Dayrens (1) , Simon Masnou (1) , Matteo Novaga (2)

1 MMCS - Modélisation mathématique, calcul scientifique
2 Dipartimento di Matematica [Pisa]

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.

Mots clés: confined curves; minimization; bending energy; elastic energy

Domaines: Optimisation et contrôle [math.OC]; Géométrie différentielle [math.DG]

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