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arXiv · 1508.05785

Existence, regularity and structure of confined elasticae

François Dayrens·Simon Masnou·Matteo Novaga
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Abstract

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.

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François Dayrens, Simon Masnou, Matteo Novaga. 2015-08-24. Existence, regularity and structure of confined elasticae. https://arxiv.org/abs/1508.05785

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