A simple proof of convergence of the Allen-Cahn equation to Brakke's motion by mean curvature Norifumi Sato 35K5749Q2053C44mean curvature flowvarifoldAllen-Cahn equation 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. Indiana University Mathematics Journal 2008 text pdf 10.1512/iumj.2008.57.3283 10.1512/iumj.2008.57.3283 en Indiana Univ. Math. J. 57 (2008) 1743 - 1752 state-of-the-art mathematics http://iumj.org/access/