A new proof of Savin's theorem on Allen–Cahn equations
Kelei Wang
Wuhan University, China
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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 regularity of flat level sets. This generalizes Allard’s -regularity theorem for stationary varifolds to the setting of Allen–Cahn equations. A new proof of Savin’s theorem on the one-dimensional symmetry of minimizers in for is also given.
Cite this article
Kelei Wang, A new proof of Savin's theorem on Allen–Cahn equations. J. Eur. Math. Soc. 19 (2017), no. 10, pp. 2997–3051
DOI 10.4171/JEMS/734