  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.
