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arXiv · 2306.14218

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

Xingzhi Bian·Yoshikazu Giga·Hiroyoshi Mitake
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Abstract

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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Xingzhi Bian, Yoshikazu Giga, Hiroyoshi Mitake. 2023-06-25. A level-set method for a mean curvature flow with a prescribed boundary. https://arxiv.org/abs/2306.14218

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