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A varifold formulation of mean curvature flow with Dirichlet or dynamic boundary conditions

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Please use this identifier to cite or link to this item:http://doi.org/10.14943/85850

Title: A varifold formulation of mean curvature flow with Dirichlet or dynamic boundary conditions
Authors: Giga, Yoshikazu Browse this author
Onoue, Fumihiko Browse this author
Takasao, Keisuke Browse this author
Issue Date: 19-Oct-2018
Publisher: Department of Mathematics, Hokkaido University
Journal Title: Hokkaido University Preprint Series in Mathematics
Volume: 1117
Start Page: 1
End Page: 45
Abstract: We consider the sharp interface limit of the Allen-Cahn equation with Dirichlet or dynamic boundary conditions and give a varifold characterization of its limit which is formally a mean curvature flow with Dirichlet or dynamic boundary conditions. In order to show the existence of the limit, we apply the phase field method under the assumption that the discrepancy measure vanishes on the boundary. For this purpose, we extend the usual Brakke flow under these boundary conditions by the first variations for varifolds on the boundary.
Type: bulletin (article)
URI: http://hdl.handle.net/2115/71694
Appears in Collections:理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics

Submitter: 数学紀要登録作業用

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