ANISOTROPIC TUBULAR NEIGHBORHOODS OF SETS

Antonin Chambolle (1) , Luca Lussardi (2) , Elena Villa (3)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 Dipartimento di Scienze Matematiche
3 Dipartimento di Matematica "Federico Enriques"

Let E ⊂ R^N be a compact set and C ⊂ R^N be a convex body with 0 ∈ int C. 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 V_E(r) := |E + rC| proving a formula for the right and the left derivatives at any r > 0 which implies that V E is of class C^1 up to a countable set completely characterized. Moreover, some properties on the second derivative of V_E are proved.

Mots clés: Rectifiability; anisotropic outer Minkowski content; viscosity solutions

Domaines: Analyse numérique [math.NA]

Antonin Chambolle, Luca Lussardi, Elena Villa. ANISOTROPIC TUBULAR NEIGHBORHOODS OF SETS. Mathematische Zeitschrift, 2021, 299 (3-4), pp.1257-1274. ⟨10.1007/s00209-021-02715-9⟩. ⟨hal-03357180⟩