# The free-boundary Brakke flow

```@article{Edelen2016TheFB,
title={The free-boundary Brakke flow},
author={Nick Edelen},
journal={Journal f{\"u}r die reine und angewandte Mathematik (Crelles Journal)},
year={2016},
volume={2020},
pages={137 - 95}
}```
• Nick Edelen
• Published 11 February 2016
• Mathematics
• Journal für die reine und angewandte Mathematik (Crelles Journal)
Abstract 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 [23] to the free-boundary setting. Using Ilmanen’s elliptic regularization procedure [10… Expand
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