Extremals for sharp Poincaré-Sobolev inequalities: periodically perforated sets and beyond
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866915637423505408 |
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| author | Brasco, Lorenzo Briani, Luca Prinari, Francesca |
| author_facet | Brasco, Lorenzo Briani, Luca Prinari, Francesca |
| contents | We consider periodically perforated unbounded open sets and prove existence of extremals for the relevant sharp Poincaré-Sobolev embedding constant. The existence result holds no matter the shape or the regularity of the hole: it is sufficient that the latter is a compact set with positive capacity. We also show how to apply the main result in order to get a similar existence statement, for sets which are periodic in some directions and bounded in all the others. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_20260 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Extremals for sharp Poincaré-Sobolev inequalities: periodically perforated sets and beyond Brasco, Lorenzo Briani, Luca Prinari, Francesca Analysis of PDEs Functional Analysis We consider periodically perforated unbounded open sets and prove existence of extremals for the relevant sharp Poincaré-Sobolev embedding constant. The existence result holds no matter the shape or the regularity of the hole: it is sufficient that the latter is a compact set with positive capacity. We also show how to apply the main result in order to get a similar existence statement, for sets which are periodic in some directions and bounded in all the others. |
| title | Extremals for sharp Poincaré-Sobolev inequalities: periodically perforated sets and beyond |
| topic | Analysis of PDEs Functional Analysis |
| url | https://arxiv.org/abs/2511.20260 |