We show that the elastic energy E(γ) of a closed curve γ has a minimizer among all plane simple regular closed curves of given enclosed area A(γ), and that the minimum is attained for a circle. The proof is of a geometric nature and deforms parts of γ in a finite number of steps to construct some related convex sets with smaller energy.
The elastica problem under area constraint / Ferone, Vincenzo; Kawohl, Bernd; Nitsch, Carlo. - In: MATHEMATISCHE ANNALEN. - ISSN 0025-5831. - 365:3-4(2016), pp. 987-1015. [10.1007/s00208-015-1284-y]
The elastica problem under area constraint
FERONE, VINCENZO;NITSCH, CARLO
2016
Abstract
We show that the elastic energy E(γ) of a closed curve γ has a minimizer among all plane simple regular closed curves of given enclosed area A(γ), and that the minimum is attained for a circle. The proof is of a geometric nature and deforms parts of γ in a finite number of steps to construct some related convex sets with smaller energy.File in questo prodotto:
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