Calculus of Variations and Geometric Measure Theory

C. Gasparetto

Epsilon-regularity for the Brakke flow with boundary

created by gasparetto on 17 Jun 2022



Inserted: 17 jun 2022
Last Updated: 17 jun 2022

Year: 2022


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. We also prove a constancy theorem for the Brakke flow.