Existence of curvature flow with forcing in a critical Sobolev space
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866909406440980480 |
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| author | Liu, Yuning Tonegawa, Yoshihiro |
| author_facet | Liu, Yuning Tonegawa, Yoshihiro |
| contents | Suppose that a closed $1$-rectifiable set $Γ_0\subset \mathbb R^2$ of finite $1$-dimensional Hausdorff measure and a vector field $u$ in a dimensionally critical Sobolev space are given. It is proved that, starting from $Γ_0$, there exists a non-trivial flow of curves with the velocity given by the sum of the curvature and the given vector field $u$. The motion law is satisfied in the sense of Brakke and the flow exists through singularities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_18284 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Existence of curvature flow with forcing in a critical Sobolev space Liu, Yuning Tonegawa, Yoshihiro Analysis of PDEs Differential Geometry 53E10, 49Q15 Suppose that a closed $1$-rectifiable set $Γ_0\subset \mathbb R^2$ of finite $1$-dimensional Hausdorff measure and a vector field $u$ in a dimensionally critical Sobolev space are given. It is proved that, starting from $Γ_0$, there exists a non-trivial flow of curves with the velocity given by the sum of the curvature and the given vector field $u$. The motion law is satisfied in the sense of Brakke and the flow exists through singularities. |
| title | Existence of curvature flow with forcing in a critical Sobolev space |
| topic | Analysis of PDEs Differential Geometry 53E10, 49Q15 |
| url | https://arxiv.org/abs/2411.18284 |