Calculus of Variations and Geometric Measure Theory

A. Chambolle - M. Morini - M. Ponsiglione

Existence and uniqueness for a crystalline mean curvature flow

created by morini on 14 Aug 2015
modified on 07 Nov 2016


Published online

Inserted: 14 aug 2015
Last Updated: 7 nov 2016

Journal: Communications on Pure and Applied Mathematics
Year: 2016
Doi: 10.1002/cpa.21668


An existence and uniqueness result, up to fattening, for a class of crystalline mean curvature flows with natural mobility is proved. The results are valid in any dimension and for arbitrary, possibly unbounded, initial closed sets. The comparison principle is obtained by means of a suitable weak formulation of the flow, while the existence of a global-in-time solution follows via a minimizing movements approach.