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.| File | Dimensione | Formato | |
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