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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
