Geodesic
A new proof of Savin's theorem on Allen–Cahn equations
Journal of the European Mathematical Society, Tome 19 (2017) no. 10, pp. 2997-3051.

Voir la notice de l'article provenant de la source EMS Press

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 C1,α regularity of flat level sets. This generalizes Allard’s ε-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 Rn for n≤7 is also given.
DOI : 10.4171/jems/734
Classification : 35-XX
Keywords: Allen–Cahn equation, phase transition, improvement of tilt-excess decay, harmonic approximation, De Giorgi conjecture 
@article{JEMS_2017_19_10_a4,
     author = {Kelei Wang},
     title = {A new proof of {Savin's} theorem on {Allen{\textendash}Cahn} equations},
     journal = {Journal of the European Mathematical Society},
     pages = {2997--3051},
     publisher = {mathdoc},
     volume = {19},
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     year = {2017},
     doi = {10.4171/jems/734},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/734/}
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Kelei Wang. A new proof of Savin's theorem on Allen–Cahn equations. Journal of the European Mathematical Society, Tome 19 (2017) no. 10, pp. 2997-3051. doi : 10.4171/jems/734. http://geodesic.mathdoc.fr/articles/10.4171/jems/734/

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