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Convergence of nonlocal geometric flows to anisotropic mean curvature motion

  • * Corresponding author: Annalisa Cesaroni

    * Corresponding author: Annalisa Cesaroni 

The authors are members and were supported by the INDAM/GNAMPA

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  • 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.

    Mathematics Subject Classification: Primary: 53E10; Secondary: 35D40, 35K93, 35R11.


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