Generic level sets in mean curvature flow are BV solutions
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866917818589511680 |
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| author | Ullrich, Anton Laux, Tim |
| author_facet | Ullrich, Anton Laux, Tim |
| contents | We show that a generic levelset of the viscosity solution to mean curvature flow is a distributional solution in the framework of sets of finite perimeter by Luckhaus and Sturzenhecker, which in addition saturates the optimal energy dissipation rate. This extends the fundamental work of Evans and Spruck (J. Geom. Anal. 1995), which draws a similar connection between the viscosity solution and Brakke flows. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_01097 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Generic level sets in mean curvature flow are BV solutions Ullrich, Anton Laux, Tim Analysis of PDEs Differential Geometry 53E10 (Primary), 35D40, 35D30 (Secondary) We show that a generic levelset of the viscosity solution to mean curvature flow is a distributional solution in the framework of sets of finite perimeter by Luckhaus and Sturzenhecker, which in addition saturates the optimal energy dissipation rate. This extends the fundamental work of Evans and Spruck (J. Geom. Anal. 1995), which draws a similar connection between the viscosity solution and Brakke flows. |
| title | Generic level sets in mean curvature flow are BV solutions |
| topic | Analysis of PDEs Differential Geometry 53E10 (Primary), 35D40, 35D30 (Secondary) |
| url | https://arxiv.org/abs/2301.01097 |