article

Title: A simple proof of convergence of the Allen-Cahn equation to Brakke's motion by mean curvature

Authors: Norifumi Sato

Issue: Volume 57 (2008), Issue 4, 1743-1752

Abstract:

$We give a simple proof that the solution of the Allen-Cahn equation converges to Brakke's motion by mean curvature, by utilizing the recent results of R\"oger and Sch\"atzle in space dimension 2 and 3. The proof avoids some of the technicalities in Ilmanen's proof.$