A new proof of Savin's theorem on Allen-Cahn equations

2014/01/25 by Wang, Kelei
#35B06 #35B08 #35B25 #35J91 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1401.6480

Abstract

In this paper we establish an improvement of tilt-excess decay estimate for the Allen-Cahn equation, and use this to give a new proof of Savin's theorem on the uniform C^1,α regularity of flat level sets, which then implies the one dimensional symmetry of minimizers in ℝⁿ for n≤ 7. This generalizes Allard's ε-regularity theorem for stationary varifolds to the setting of Allen-Cahn equations.

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