Convergence of nonlocal geometric flows to anisotropic mean curvature motion

@article{Cesaroni2018ConvergenceON,
  title={Convergence of nonlocal geometric flows to anisotropic mean curvature motion},
  author={Annalisa Cesaroni and Valerio Pagliari},
  journal={arXiv: Analysis of PDEs},
  year={2018}
}
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… Expand
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