Existence of the classical solution to the fractional mean curvature flow with capillary-type boundary conditions
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866910015610159104 |
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| author | Fan, Linlin Zhao, Peibiao |
| author_facet | Fan, Linlin Zhao, Peibiao |
| contents | Wang, Weng and Xia[Math. Ann. 388 (2024), no. 2] studied a mean curvature type flow for the smooth, embedded capillary hypersurfaces with a constant contact angle $θ\in(0,π)$ and confirmed the existence of solutions by the standard PDE theory. In the present paper, we study a fractional mean curvature flow for $C^{1,1}$-regular hypersurfaces with a capillary-type boundary condition and obtain the short time existence by the fixed point argument. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_07989 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Existence of the classical solution to the fractional mean curvature flow with capillary-type boundary conditions Fan, Linlin Zhao, Peibiao Differential Geometry Analysis of PDEs Wang, Weng and Xia[Math. Ann. 388 (2024), no. 2] studied a mean curvature type flow for the smooth, embedded capillary hypersurfaces with a constant contact angle $θ\in(0,π)$ and confirmed the existence of solutions by the standard PDE theory. In the present paper, we study a fractional mean curvature flow for $C^{1,1}$-regular hypersurfaces with a capillary-type boundary condition and obtain the short time existence by the fixed point argument. |
| title | Existence of the classical solution to the fractional mean curvature flow with capillary-type boundary conditions |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2602.07989 |