On an obstacle problem for the Brakke flow with a generalized right-angle boundary condition
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914741980495872 |
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| author | Nik, Katerina Takasao, Keisuke |
| author_facet | Nik, Katerina Takasao, Keisuke |
| contents | We study Brakke's mean curvature flow with obstacles and with a right-angle boundary condition. Assuming that the obstacles have $C^{1,1}$-boundaries we prove that a weak solution exists globally in time. To show the existence we apply the phase-field method and thus investigate the singular limit of the Allen-Cahn equation with forcing term and homogeneous Neumann bounday condition. We also construct sub- and supersolutions that correspond to the obstacles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_03763 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On an obstacle problem for the Brakke flow with a generalized right-angle boundary condition Nik, Katerina Takasao, Keisuke Analysis of PDEs 28A75, 35K20, 53E10 We study Brakke's mean curvature flow with obstacles and with a right-angle boundary condition. Assuming that the obstacles have $C^{1,1}$-boundaries we prove that a weak solution exists globally in time. To show the existence we apply the phase-field method and thus investigate the singular limit of the Allen-Cahn equation with forcing term and homogeneous Neumann bounday condition. We also construct sub- and supersolutions that correspond to the obstacles. |
| title | On an obstacle problem for the Brakke flow with a generalized right-angle boundary condition |
| topic | Analysis of PDEs 28A75, 35K20, 53E10 |
| url | https://arxiv.org/abs/2404.03763 |