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Anisotropic and crystalline mean curvature flow of mean-convex sets

Chambolle, Antonin; Novaga, Matteo (2022), Anisotropic and crystalline mean curvature flow of mean-convex sets, Annali della Scuola Normale Superiore di Pisa, XXIII, 2, p. 623-643. 10.2422/2036-2145.202005_009

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Type
Article accepté pour publication ou publié
Date
2022
Journal name
Annali della Scuola Normale Superiore di Pisa
Volume
XXIII
Number
2
Publisher
Scuola normale superiore
Pages
623-643
Publication identifier
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Author(s)
Chambolle, Antonin
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Novaga, Matteo
Dipartimento di Matematica Pura e Applicata [Padova]
Abstract (EN)
We consider a variational scheme for the anisotropic (including crystalline) mean curvature flow of sets with strictly positive anisotropic mean curvature. We show that such condition is preserved by the scheme, and we prove the strict convergence in BV of the time-integrated perimeters of the approximating evolutions, extending a recent result of De Philippis and Laux to the anisotropic setting. We also prove uniqueness of the flat flow obtained in the limit.
Subjects / Keywords
Anisotropic mean curvature flow; crystal growth; minimizing movements; mean convexity; arrival time; 1-superharmonic functions