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Inserted: 5 nov 2018
Last Updated: 13 nov 2026

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

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 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.

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