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

Giga, Yoshikazu; Onoue, Fumihiko; Takasao, Keisuke

Hokkaido University Preprint Series in Mathematics, 2018, 1117, 1-45

Permalink : https://doi.org/10.14943/85850

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アクセス権	open access
DOI	https://doi.org/10.14943/85850
URI	https://hdl.handle.net/2115/71694
タイトル	A varifold formulation of mean curvature ﬂow with Dirichlet or dynamic boundary conditions
著者	Giga, Yoshikazu ; Onoue, Fumihiko ; Takasao, Keisuke
著者名 Giga, Yoshikazu
著者名 Onoue, Fumihiko
著者名 Takasao, Keisuke
言語	英語
発行日	2018-10-19
出版者	Department of Mathematics, Hokkaido University
収録物名	Hokkaido University Preprint Series in Mathematics
巻(号)	1117
ページ	1-45
抄録	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.
資源タイプ	紀要論文
出版タイプ	Version of Record