Time global existence of generalized BV flow via the Allen--Cahn equation

Abstract

We show that a mean curvature flow obtained as the limit of the Allen--Cahn equation is not only a Brakke flow but also a generalized BV flow proposed by Stuvard and Tonegawa.

15 pages. This paper draws heavily from arXiv:2305.12374. I have fixed minor mistakes. To appear in Interfaces Free Bound