Minimizing Movements for Mean Curvature Flow of Partitions
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 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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Information & Authors
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Published In
SIAM Journal on Mathematical Analysis
Pages: 4117 - 4148
DOI: 10.1137/17M1159294
ISSN (online): 1095-7154
Copyright
© 2018, Society for Industrial and Applied Mathematics.
History
Submitted: 30 November 2017
Accepted: 2 May 2018
Published online: 24 July 2018
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Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni https://doi.org/10.13039/100012740
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