Let E⊂ RN be a compact set and C⊂ RN be a convex body with 0∈intC. We prove that the topological boundary of the anisotropic enlargement E+ rC is contained in a finite union of Lipschitz surfaces. We also investigate the regularity of the volume function VE(r) : = | E+ rC| proving a formula for the right and the left derivatives at any r> 0 which implies that VE is of class C1 up to a countable set completely characterized. Moreover, some properties on the second derivative of VE are proved.

Anisotropic tubular neighborhoods of sets / A. Chambolle, L. Lussardi, E. Villa. - In: MATHEMATISCHE ZEITSCHRIFT. - ISSN 0025-5874. - 299:3-4(2021 Dec), pp. 1257-1274. [10.1007/s00209-021-02715-9]

Anisotropic tubular neighborhoods of sets

E. Villa
2021-12

Abstract

Let E⊂ RN be a compact set and C⊂ RN be a convex body with 0∈intC. We prove that the topological boundary of the anisotropic enlargement E+ rC is contained in a finite union of Lipschitz surfaces. We also investigate the regularity of the volume function VE(r) : = | E+ rC| proving a formula for the right and the left derivatives at any r> 0 which implies that VE is of class C1 up to a countable set completely characterized. Moreover, some properties on the second derivative of VE are proved.
anisotropic outer Minkowski content; Rectifiability; viscosity solutions
Settore MAT/05 - Analisi Matematica
8-mar-2021
Article (author)
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/867095
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