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Minimizing movements for forced anisotropic mean curvature flow of partitions with mobilities

Bellettini, Giovanni; Chambolle, Antonin; Kholmatov, Shokhrukh (2021), Minimizing movements for forced anisotropic mean curvature flow of partitions with mobilities, Proceedings of the Royal Society of Edinburgh. Section A, Mathematical and Physical Sciences, 151, 4, p. 1135-1170. 10.1017/prm.2020.53

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Type
Article accepté pour publication ou publié
Date
2021
Journal name
Proceedings of the Royal Society of Edinburgh. Section A, Mathematical and Physical Sciences
Volume
151
Number
4
Publisher
Cambridge University Press
Pages
1135-1170
Publication identifier
Metadata
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Author(s)
Bellettini, Giovanni
Dipartimento di Matematica e Informatica [Siena]
Chambolle, Antonin cc
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Kholmatov, Shokhrukh
University of Vienna [Vienna]
Abstract (EN)
Under suitable assumptions on the family of anisotropies, we prove the existence of a weak global 1/(n+1)-Hölder continuous in time mean curvature flow with mobilities of a bounded anisotropic partition in any dimension using the method of minimizing movements. The result is extended to the case when suitable driving forces are present. We improve the Hölder exponent to 1/2 in the case of partitions with the same anisotropy and the same mobility and provide a weak comparison result in this setting for a weak anisotropic mean curvature flow of a partition and an anisotropic mean curvature two-phase flow.
Subjects / Keywords
mean curvature flow; partitions; minimizing movements; forcing; anisotropy; mobility