Vol. 12, No. 3, 2019

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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

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.

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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
Received: 10 November 2017
Revised: 4 May 2018
Accepted: 29 June 2018
Published: 7 October 2018
Antonin Chambolle
École Polytechnique, CNRS
Universé Paris-Saclay
Massimiliano Morini
Dipartimento di Matematica
Università degli Studi di Parma
Matteo Novaga
Dipartimento di Matematica
Università di Pisa
Marcello Ponsiglione
Dipartimento di Matematica
Sapienza Università di Roma