抄録
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.
収録刊行物
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- Hokkaido University Preprint Series in Mathematics
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Hokkaido University Preprint Series in Mathematics 1151 1-26, 2023-06-29
Department of Mathematics, Hokkaido University
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詳細情報 詳細情報について
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- CRID
- 1390578141487603968
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- DOI
- 10.14943/107831
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- HANDLE
- 2115/90094
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- 本文言語コード
- en
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- データソース種別
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- JaLC
- IRDB
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- 抄録ライセンスフラグ
- 使用可