A simple proof of convergence of the Allen-Cahn equation to Brakke's motion by mean curvature
Norifumi Sato · Indiana University Mathematics Journal · 2008
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 Roger and Schatzle in space dimension 2 and 3. The proof avoids some of the technicalities in Ilmanen's proof.