Vol. 12, No. 3, 2019

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ISSN: 1948-206X (e-only)
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Generalized crystalline evolutions as limits of flows with smooth anisotropies

Antonin Chambolle, Massimiliano Morini, Matteo Novaga and Marcello Ponsiglione

Vol. 12 (2019), No. 3, 789–813
Abstract

We prove existence and uniqueness of weak solutions to anisotropic and crystalline mean curvature flows, obtained as a limit of the viscosity solutions to flows with smooth anisotropies.

Keywords
geometric evolution equations, crystalline mean curvature flow, level-set formulation, nonlocal curvature flows, nonlocal geometric flows, minimizing movements, viscosity solutions
Mathematical Subject Classification 2010
Primary: 53C44, 49M25, 35D40
Milestones
Received: 10 November 2017
Revised: 4 May 2018
Accepted: 29 June 2018
Published: 7 October 2018
Authors
Antonin Chambolle
CMAP
École Polytechnique, CNRS
Universé Paris-Saclay
Palaiseau
France
Massimiliano Morini
Dipartimento di Matematica
Università degli Studi di Parma
Parma
Italy
Matteo Novaga
Dipartimento di Matematica
Università di Pisa
Pisa
Italy
Marcello Ponsiglione
Dipartimento di Matematica
Sapienza Università di Roma
Roma
Italy