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arXiv · 1811.01732

Convergence of nonlocal geometric flows to anisotropic mean curvature motion

Annalisa Cesaroni·Valerio Pagliari
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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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Annalisa Cesaroni, Valerio Pagliari. 2018-11-05. Convergence of nonlocal geometric flows to anisotropic mean curvature motion. https://doi.org/10.3934/dcds.2021065

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