Calculus of Variations and Geometric Measure Theory
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G. Bellettini - S. Kholmatov

Minimizing movements for mean curvature flow of partitions

created by kholmatov on 04 Feb 2017

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Submitted Paper

Inserted: 4 feb 2017
Last Updated: 4 feb 2017

Year: 2017

Abstract:

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 show that the minimizing movement solution starting from a partition made by a union of bounded convex sets at a positive distance agrees with the classical mean curvature flow, and the motion is stable with respect to the Hausdorff convergence of the initial partition.

Tags: GeMeThNES
Keywords: minimizing movements, mean curvature flow, partitions


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