Nonlocal free boundary minimal surfaces
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909715870515200 |
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| author | Badran, Marco Dipierro, Serena Valdinoci, Enrico |
| author_facet | Badran, Marco Dipierro, Serena Valdinoci, Enrico |
| contents | We introduce the nonlocal analogue of the classical free boundary minimal hypersurfaces in an open domain $Ω$ of $\mathbb{R}^n$ as the (boundaries of) critical points of the fractional perimeter $\operatorname{Per}_s(\cdot,\,Ω)$ with respect to inner variations leaving $Ω$ invariant. We deduce the Euler-Lagrange equations and prove a few surprising features, such as the existence of critical points without boundary and a strong volume constraint in $Ω$ for unbounded hypersurfaces. Moreover, we investigate stickiness properties and regularity across the boundary. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_00337 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nonlocal free boundary minimal surfaces Badran, Marco Dipierro, Serena Valdinoci, Enrico Analysis of PDEs Differential Geometry 49Q05, 35R11, 35R35, 49Q10 We introduce the nonlocal analogue of the classical free boundary minimal hypersurfaces in an open domain $Ω$ of $\mathbb{R}^n$ as the (boundaries of) critical points of the fractional perimeter $\operatorname{Per}_s(\cdot,\,Ω)$ with respect to inner variations leaving $Ω$ invariant. We deduce the Euler-Lagrange equations and prove a few surprising features, such as the existence of critical points without boundary and a strong volume constraint in $Ω$ for unbounded hypersurfaces. Moreover, we investigate stickiness properties and regularity across the boundary. |
| title | Nonlocal free boundary minimal surfaces |
| topic | Analysis of PDEs Differential Geometry 49Q05, 35R11, 35R35, 49Q10 |
| url | https://arxiv.org/abs/2508.00337 |