Existence, regularity and structure of confined elasticae
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چکیده
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.
منابع مشابه
Existence, regularity and structure of con ned elasticae
We consider the problem of minimizing the bending or elastic energy among Jordan curves con ned 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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تاریخ انتشار 2017