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

• Autores: Norifumi Sato
• Localización: Indiana university mathematics journal, ISSN 0022-2518, Vol. 57, Nº 4, 2008, págs. 1743-1752
• Idioma: inglés
• DOI: 10.1512/iumj.2008.57.3283
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• Resumen

  • 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 Röger and Schätzle in space dimension 2 and 3. The proof avoids some of the technicalities in Ilmanen's proof.