Calculus of Variations and Geometric Measure Theory

A. Cesaroni - V. Pagliari

Convergence of nonlocal geometric flows to anisotropic mean curvature motion

created by pagliari on 05 Nov 2018
modified by cesaroni on 01 Jul 2021


Published Paper

Inserted: 5 nov 2018
Last Updated: 1 jul 2021

Journal: Discrete & Continuous Dynamical Systems - A
Volume: 41
Number: 10
Pages: 4987-5008
Year: 2021

ArXiv: 1811.01732 PDF


We consider nonlocal curvature functionals associated with positive interaction kernels, and we show that local anisotropic mean curvature functionals can be retrieved in a blow-up 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 set-theoretic approach related to the theory of De Giorgi’s barriers for evolution equations.