Existence of BV flow via elliptic regularization

Abstract

We investigate a mean curvature flow obtained via elliptic regularization, and prove that it is not only a Brakke flow, but additionally a generalized BV flow proposed by Stuvard and Tonegawa. In particular, we show that the change in volume of the evolving phase can be expressed in terms of the generalized mean curvature of the Brakke flow.

19 pages, I fixed minor mistakes. To appear in Hiroshima math. J

References in corpus (1)

• Stochastic Allen-Cahn approximation of the mean curvature flow: large deviations upper bound