The isoperimetric inequality for the capillary energy outside convex cylinders
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866915499725553664 |
|---|---|
| author | Fusco, Nicola Julin, Vesa Morini, Massimiliano |
| author_facet | Fusco, Nicola Julin, Vesa Morini, Massimiliano |
| contents | We study the isoperimetric problem for capillary surfaces with a general contact angle $θ\in (0, π)$, outside convex infinite cylinders with arbitrary two-dimensional convex section. We prove that the capillary energy of any surface supported on any such convex cylinder is strictly larger than that of a spherical cap with the same volume and the same contact angle on a flat support, unless the surface is itself a spherical cap resting on a facet of the cylinder. In this class of convex sets, our result extends for the first time the well-known Choe-Ghomi-Ritoré relative isoperimetric inequality, corresponding to the case $θ= π/2$, to general angles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_19011 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The isoperimetric inequality for the capillary energy outside convex cylinders Fusco, Nicola Julin, Vesa Morini, Massimiliano Analysis of PDEs We study the isoperimetric problem for capillary surfaces with a general contact angle $θ\in (0, π)$, outside convex infinite cylinders with arbitrary two-dimensional convex section. We prove that the capillary energy of any surface supported on any such convex cylinder is strictly larger than that of a spherical cap with the same volume and the same contact angle on a flat support, unless the surface is itself a spherical cap resting on a facet of the cylinder. In this class of convex sets, our result extends for the first time the well-known Choe-Ghomi-Ritoré relative isoperimetric inequality, corresponding to the case $θ= π/2$, to general angles. |
| title | The isoperimetric inequality for the capillary energy outside convex cylinders |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2406.19011 |