We prove the density of polyhedral partitions in the set of finite Caccioppoli partitions. Precisely, given a decomposition u of a bounded Lipschitz set Ω ⊂ Rn into finitely many subsets of finite perimeter and ε> 0 , we prove that u is ε-close to a small deformation of a polyhedral decomposition vε, in the sense that there is a C1 diffeomorphism fε: Rn→ Rn which is ε-close to the identity and such that u∘ fε- vε is ε-small in the strong BV norm. This implies that the energy of u is close to that of vε for a large class of energies defined on partitions.

Braides, A., Conti, S., Garroni, A. (2017). Density of polyhedral partitions. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 56(2) [10.1007/s00526-017-1108-x].

Density of polyhedral partitions

Braides, Andrea
;
2017-01-01

Abstract

We prove the density of polyhedral partitions in the set of finite Caccioppoli partitions. Precisely, given a decomposition u of a bounded Lipschitz set Ω ⊂ Rn into finitely many subsets of finite perimeter and ε> 0 , we prove that u is ε-close to a small deformation of a polyhedral decomposition vε, in the sense that there is a C1 diffeomorphism fε: Rn→ Rn which is ε-close to the identity and such that u∘ fε- vε is ε-small in the strong BV norm. This implies that the energy of u is close to that of vε for a large class of energies defined on partitions.
2017
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/05 - ANALISI MATEMATICA
English
Con Impact Factor ISI
49J45; 49Q15; 49Q20; Analysis; Applied Mathematics
http://link.springer-ny.com/link/service/journals/00526/index.htm
Braides, A., Conti, S., Garroni, A. (2017). Density of polyhedral partitions. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 56(2) [10.1007/s00526-017-1108-x].
Braides, A; Conti, S; Garroni, A
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/211704
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