Calculus of Variations and Geometric Measure Theory

C. Gasparetto

Epsilon-regularity for the Brakke flow with boundary

created by gasparetto on 17 Jun 2022
modified on 07 Feb 2024


Accepted Paper

Inserted: 17 jun 2022
Last Updated: 7 feb 2024

Journal: Analysis & PDE
Year: 2022

ArXiv: 2206.08830 PDF


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.