On non-local almost minimal sets and an application to the non-local Massari's Problem
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914204780331008 |
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| author | Dipierro, Serena Valdinoci, Enrico Villa, Riccardo |
| author_facet | Dipierro, Serena Valdinoci, Enrico Villa, Riccardo |
| contents | We consider a fractional Plateau's problem dealing with sets with prescribed non-local mean curvature. This problem can be seen as a non-local counterpart of the classical Massari's Problem. We obtain existence and regularity results, relying on a suitable version of the non-local theory for almost minimal sets. In this framework, the fractional curvature term in the energy functional can be interpreted as a perturbation of the fractional perimeter. In addition, we also discuss stickiness phenomena for non-local almost minimal sets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_07727 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On non-local almost minimal sets and an application to the non-local Massari's Problem Dipierro, Serena Valdinoci, Enrico Villa, Riccardo Analysis of PDEs We consider a fractional Plateau's problem dealing with sets with prescribed non-local mean curvature. This problem can be seen as a non-local counterpart of the classical Massari's Problem. We obtain existence and regularity results, relying on a suitable version of the non-local theory for almost minimal sets. In this framework, the fractional curvature term in the energy functional can be interpreted as a perturbation of the fractional perimeter. In addition, we also discuss stickiness phenomena for non-local almost minimal sets. |
| title | On non-local almost minimal sets and an application to the non-local Massari's Problem |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2411.07727 |