Epsilon-regularity for the Brakke flow with boundary
Copyright policy )Epsilon-regularity for the Brakke flow with boundary
We prove that, if a Brakke flow with boundary is close enough to a stationary half-plane with density one, then it is $C^{1,α}$. 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.
The constancy theorem was removed. Final version to appear in Analysis & PDE
Mathematics - Differential Geometry, Brakke flows, \(\varepsilon\)-regularity, Smoothness and regularity of solutions to PDEs, Flows related to mean curvature, small perturbation solutions, Viscosity solutions to PDEs, 53E10 (Primary) 35D40, 35B65 (Secondary), varifolds, boundary regularity, Mathematics - Analysis of PDEs, Differential Geometry (math.DG), Brakke's theorem, viscosity, FOS: Mathematics, mean curvature flows, Allard's theorem, Analysis of PDEs (math.AP)
Mathematics - Differential Geometry, Brakke flows, \(\varepsilon\)-regularity, Smoothness and regularity of solutions to PDEs, Flows related to mean curvature, small perturbation solutions, Viscosity solutions to PDEs, 53E10 (Primary) 35D40, 35B65 (Secondary), varifolds, boundary regularity, Mathematics - Analysis of PDEs, Differential Geometry (math.DG), Brakke's theorem, viscosity, FOS: Mathematics, mean curvature flows, Allard's theorem, Analysis of PDEs (math.AP)
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