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 movement approach.
Existence and Uniqueness for a Crystalline Mean Curvature Flow / Chambolle, Antonin; Morini, Massimiliano; Ponsiglione, Marcello. - In: COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS. - ISSN 0010-3640. - 70:6(2017), pp. 1084-1114. [10.1002/cpa.21668]