Calculus of Variations and Geometric Measure Theory
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A. Cesaroni - V. Pagliari

Convergence of nonlocal geometric flows to anisotropic mean curvature motion

created by pagliari on 05 Nov 2018

[BibTeX]

Preprint

Inserted: 5 nov 2018
Last Updated: 5 nov 2018

Year: 2018

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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