In this paper a Blaschke-Santal'o diagram involving the area, the perimeter and the elastic energy of planar convex bodies is considered. In order to do this, we investigate the following shape optimization problem: minΩ∈C{E(Ω)+μA(Ω)}, where C is the class of convex bodies with fixed perimeter and μ≥0 is a parameter, A is the area and E is the elastic energy, that is a Willmore type energy in the plane. Existence, regularity and geometric properties of solutions to this minimum problem are shown.

Elastic Energy of a convex body / Chiara Bianchini; Antoine Henrot; Takeo Takahashi. - In: MATHEMATISCHE NACHRICHTEN. - ISSN 0025-584X. - STAMPA. - 289:(2016), pp. 546-574. [10.1002/mana.201400256]

Elastic Energy of a convex body

BIANCHINI, CHIARA;
2016

Abstract

In this paper a Blaschke-Santal'o diagram involving the area, the perimeter and the elastic energy of planar convex bodies is considered. In order to do this, we investigate the following shape optimization problem: minΩ∈C{E(Ω)+μA(Ω)}, where C is the class of convex bodies with fixed perimeter and μ≥0 is a parameter, A is the area and E is the elastic energy, that is a Willmore type energy in the plane. Existence, regularity and geometric properties of solutions to this minimum problem are shown.
2016
289
546
574
Chiara Bianchini; Antoine Henrot; Takeo Takahashi
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/1003692
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