Geodesic
A new isoperimetric inequality for the elasticae
Journal of the European Mathematical Society, Tome 19 (2017) no. 11, pp. 3355-3376.

Voir la notice de l'article provenant de la source EMS Press

For a smooth curve γ, we define its elastic energy as E(γ)=21​∫γ​k2(s)ds where k(s) is the curvature. The main purpose of the paper is to prove that among all smooth, simply connected, bounded open sets of prescribed area in R2, the disc has the boundary with the least elastic energy. In other words, for any bounded simply connected domain Ω, the following isoperimetric inequality holds: E2(∂Ω)A(Ω)≥π3. The analysis relies on the minimization of the elastic energy of drops enclosing a prescribed area, for which we give as well an analytic answer.
DOI : 10.4171/jems/740
Classification : 49-XX, 51-XX, 53-XX
Keywords: Euler elasticae, minimization of elastic energy, isoperimetric inequality, curvature 
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     author = {Dorin Bucur and Antoine Henrot},
     title = {A new isoperimetric inequality for the elasticae},
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Dorin Bucur; Antoine Henrot. A new isoperimetric inequality for the elasticae. Journal of the European Mathematical Society, Tome 19 (2017) no. 11, pp. 3355-3376. doi : 10.4171/jems/740. http://geodesic.mathdoc.fr/articles/10.4171/jems/740/

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