We prove the existence of a weak global in time mean curvature flow of a bounded partition of space using the method of minimizing movements. The result is extended to the case when suitable driving forces are present. We also prove some consistency results for a minimizing movement solution with smooth and viscosity solutions when the evolution starts from a partition made by a union of bounded sets at a positive distance. In addition, the motion starting from the union of convex sets at a positive distance agrees with the classical mean curvature flow and is stable with respect to the Hausdorff convergence of the initial partitions.
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|Titolo:||Minimizing movements for mean curvature flow of partitions|
|Citazione:||Bellettini, G., & Kholmatov, S.Y. (2018). Minimizing movements for mean curvature flow of partitions. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 50(4), 4117-4148.|
|Appare nelle tipologie:||1.1 Articolo in rivista|