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January/February 2021 A varifold formulation of mean curvature flow with Dirichlet or dynamic boundary conditions
Yoshikazu Giga, Fumihiko Onoue, Keisuke Takasao
Differential Integral Equations 34(1/2): 21-126 (January/February 2021).

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 vanishing on the boundary and some uniform boundedness property of the discrepancy measure. For this purpose, we extend the usual Brakke flow under these boundary conditions by the first variations for varifolds on the boundary.

Citation

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Yoshikazu Giga. Fumihiko Onoue. Keisuke Takasao. "A varifold formulation of mean curvature flow with Dirichlet or dynamic boundary conditions." Differential Integral Equations 34 (1/2) 21 - 126, January/February 2021.

Information

Published: January/February 2021
First available in Project Euclid: 12 January 2021

MathSciNet: MR4198540

Subjects:
Primary: 35A15, 35D30, 35K20, 49Q20

Rights: Copyright © 2021 Khayyam Publishing, Inc.

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Vol.34 • No. 1/2 • January/February 2021
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