Compactness and local regularity for free boundary Brakke flows
Year: 2016
Type: preprint
Abstract: We define a notion of Brakke flow with free-boundary in a barrier surface, and prove this class admits compactness. We find we must weaken the original notion of Brakke flows to allow for instantaneous stopping at the barrier. We 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. Finally, we show Ilmanen's elliptic regularization procedure extends to free-boundary Brakke flows.
Source: arXiv (Cornell University)
Author: Nick Edelen
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2261832714