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A new proof of Savin's theorem on Allen-Cahn equations
- Publication Year :
- 2014
-
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 $C^{1,\alpha}$ regularity of flat level sets, which then implies the one dimensional symmetry of minimizers in $\mathbb{R}^n$ for $n\leq 7$. This generalizes Allard's $\varepsilon$-regularity theorem for stationary varifolds to the setting of Allen-Cahn equations.<br />Comment: 63 pages, author's final version. To appear in J. Eur. Math. Soc
- Subjects :
- Mathematics - Analysis of PDEs
35B06, 35B06, 35B08, 35B25, 35J91
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1401.6480
- Document Type :
- Working Paper