Geometric criteria for the existence of capillary surfaces in tubes
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929263852126208 |
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| author | Saracco, Giorgio |
| author_facet | Saracco, Giorgio |
| contents | We review some geometric criteria and prove a refined version, that yield existence of capillary surfaces in tubes $Ω\times \mathbb{R}$ in a gravity free environment, in the case of physical interest, that is, for bounded, open, and simply connected $Ω\subset \mathbb{R}^2$. These criteria rely on suitable weak one-sided bounds on the curvature of the boundary of the cross-section $Ω$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_17330 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Geometric criteria for the existence of capillary surfaces in tubes Saracco, Giorgio Analysis of PDEs 49K20, 35J93, 49Q10, 49Q20 We review some geometric criteria and prove a refined version, that yield existence of capillary surfaces in tubes $Ω\times \mathbb{R}$ in a gravity free environment, in the case of physical interest, that is, for bounded, open, and simply connected $Ω\subset \mathbb{R}^2$. These criteria rely on suitable weak one-sided bounds on the curvature of the boundary of the cross-section $Ω$. |
| title | Geometric criteria for the existence of capillary surfaces in tubes |
| topic | Analysis of PDEs 49K20, 35J93, 49Q10, 49Q20 |
| url | https://arxiv.org/abs/2402.17330 |