Calculus of Variations and Geometric Measure Theory
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S. Stuvard - Y. Tonegawa

On the existence of canonical multi-phase Brakke flows

created by stuvard on 06 Oct 2021



Inserted: 6 oct 2021
Last Updated: 6 oct 2021

Year: 2021

ArXiv: 2109.14415 PDF


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. Under suitable assumptions on the initial datum, such additional property resolves the non-uniqueness issue of Brakke flows.


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