A note on non-local Sobolev spaces and non-local perimeters
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866910906702626816 |
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| author | Bessas, Konstantinos Brusca, Giuseppe Cosma |
| author_facet | Bessas, Konstantinos Brusca, Giuseppe Cosma |
| contents | We investigate the space of non-local Sobolev functions associated with an integral kernel. We prove an extension result, Sobolev and Poincaré inequalities and an isoperimetric inequality for the non-local perimeter restricted to a set. Finally, we remark on non-local isoperimetric problems, even when the underlying kernel is not necessarily radially symmetric. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_06236 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A note on non-local Sobolev spaces and non-local perimeters Bessas, Konstantinos Brusca, Giuseppe Cosma Functional Analysis Analysis of PDEs 49Q20, 26B30, 46E35 We investigate the space of non-local Sobolev functions associated with an integral kernel. We prove an extension result, Sobolev and Poincaré inequalities and an isoperimetric inequality for the non-local perimeter restricted to a set. Finally, we remark on non-local isoperimetric problems, even when the underlying kernel is not necessarily radially symmetric. |
| title | A note on non-local Sobolev spaces and non-local perimeters |
| topic | Functional Analysis Analysis of PDEs 49Q20, 26B30, 46E35 |
| url | https://arxiv.org/abs/2504.06236 |