open access

https://doi.org/10.14943/107831

https://hdl.handle.net/2115/90094

A level-set method for a mean curvature flow with a prescribed boundary

英語

obstacle problem

2023-06-29

Department of Mathematics, Hokkaido University

Hokkaido University Preprint Series in Mathematics

1151

1-26

We propose a level-set method for a mean curvature flow whose boundary is prescribed by interpreting the boundary as an obstacle. Since the corresponding obstacle problem is globally solvable, our method gives a global-in-time level-set mean curvature flow under a prescribed boundary with no restriction of the profile of an initial hypersurface. We show that our solution agrees with a classical mean curvature flow under the Dirichlet condition. We moreover prove that our solution agrees with a level-set flow under the Dirichlet condition constructed by P. Sternberg and W. P. Ziemer (1994), where the initial hypersurface is contained in a strictly mean-convex domain and the prescribed boundary is on the boundary of the domain.

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