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.

Density of polyhedral partitions / Braides, A.; Conti, S.; Garroni, A.. - In: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0944-2669. - 56:2(2017), pp. 1-10. [10.1007/s00526-017-1108-x]

Density of polyhedral partitions

Braides A.;Conti S.;Garroni A.
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
56
2
1
10
28
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/20.500.11767/139461
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