Epsilon-regularity for the Brakke flow with boundary

Abstract

We prove that, if a Brakke flow with boundary is close enough to a stationary half-plane with density one, then it is $C^{1,\alpha }$. Our approach is based on viscosity techniques introduced by Savin in the context of elliptic equations. The same techniques can be used to give a proof of Brakke's (interior) regularity theorem which is alternative to the original one.

The constancy theorem was removed. Final version to appear in Analysis & PDE

References in corpus (1)

• End-time regularity theorem for Brakke flows