Premium
Existence and Uniqueness for a Crystalline Mean Curvature Flow
Author(s) -
Chambolle Antonin,
Morini Massimiliano,
Ponsiglione Marcello
Publication year - 2017
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.21668
Subject(s) - uniqueness , mean curvature flow , mathematics , mean curvature , flow (mathematics) , curvature , dimension (graph theory) , class (philosophy) , mathematical analysis , geometric flow , pure mathematics , geometry , computer science , artificial intelligence
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.© 2016 Wiley Periodicals, Inc.