  We develop the notion of Brakke flow with free-boundary in a barrier surface.
Unlike the classical free-boundary mean curvature flow, the free-boundary
Brakke flow must "pop" upon tangential contact with the barrier. We prove a
compactness theorem for free-boundary Brakke flows, define a Gaussian
monotonicity formula valid at all points, and use this to adapt the local
regularity theorem of White to the free-boundary setting. We use Ilmanen's
elliptic regularization procedure to prove existence of free-boundary Brakke
flows.
