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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.11520 |
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| _version_ | 1866913026094923776 |
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| author | Bucur, Claudia Lombardini, Luca |
| author_facet | Bucur, Claudia Lombardini, Luca |
| contents | In this paper, we introduce a functional and a geometric setting for an obstacle problem for nonlocal minimal graphs. In particular we study existence of solutions, a priori estimates, and we prove the equivalence of the two settings. We then observe a striking stickiness phenomena when the fractional parameter is small and the data at infinity is not too large: the nonlocal minimal graphs adhere entirely to the obstacle and leave the remainder of the domain asymptotically empty. We thus provide a class of examples where continuity of nonlocal minimal graphs across the boundary and across the obstacle may fail. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_11520 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Asymptotics as $s\searrow 0$ of the nonlocal nonparametric Plateau problem with obstacles Bucur, Claudia Lombardini, Luca Analysis of PDEs In this paper, we introduce a functional and a geometric setting for an obstacle problem for nonlocal minimal graphs. In particular we study existence of solutions, a priori estimates, and we prove the equivalence of the two settings. We then observe a striking stickiness phenomena when the fractional parameter is small and the data at infinity is not too large: the nonlocal minimal graphs adhere entirely to the obstacle and leave the remainder of the domain asymptotically empty. We thus provide a class of examples where continuity of nonlocal minimal graphs across the boundary and across the obstacle may fail. |
| title | Asymptotics as $s\searrow 0$ of the nonlocal nonparametric Plateau problem with obstacles |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2604.11520 |