Affiliation:
1. Dipartimento di Matematica , Università degli Studi di Milano , Via Saldini 50, 20133 Milano (MI) , Italy
2. Department of Mathematics , Tokyo Institute of Technology , 2-12-1 Ookayama, Meguro-ku , Tokyo 152-8551 , Japan
Abstract
Abstract
This paper establishes the global-in-time existence of a multi-phase mean curvature flow, evolving from an arbitrary closed rectifiable initial datum, which is a Brakke flow and a BV solution at the same time. In particular, we prove the validity of an explicit identity concerning the change of volume of the evolving grains, showing that their boundaries move according to the generalized mean curvature vector of the Brakke flow.
As a consequence of the results recently established in
[J. Fischer, S. Hensel, T. Laux and T. M. Simon,
The local structure of the energy landscape in multiphase mean curvature flow: Weak-strong uniqueness and stability of evolutions,
preprint 2020, https://arxiv.org/abs/2003.05478],
under suitable assumptions on the initial datum, such additional property resolves the non-uniqueness issue of Brakke flows.
Funder
Japan Society for the Promotion of Science
Subject
Applied Mathematics,Analysis
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