Convergence of nonlocal geometric flows to anisotropic mean curvature motion
Abstract
We consider nonlocal curvature functionals associated with positive interaction kernels, and we show that local anisotropic mean curvature functionals can be retrieved in a blowup limit from them. As a consequence, we prove that the viscosity solutions to the rescaled nonlocal geometric flows locally uniformly converge to the viscosity solution to the anisotropic mean curvature motion. The result is achieved by combining a compactness argument and a settheoretic approach related to the theory of De Giorgi's barriers for evolution equations.
 Publication:

arXiv eprints
 Pub Date:
 November 2018
 arXiv:
 arXiv:1811.01732
 Bibcode:
 2018arXiv181101732C
 Keywords:

 Mathematics  Analysis of PDEs;
 53E10;
 35D40;
 35K93;
 35R11
 EPrint:
 21 pages