Interacting free boundaries in obstacle problems
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915141220564992 |
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| author | Araújo, Damião J. Teymurazyan, Rafayel |
| author_facet | Araújo, Damião J. Teymurazyan, Rafayel |
| contents | We study obstacle problems governed by two distinct types of diffusion operators involving interacting free boundaries. We obtain a somewhat surprising coupling property, leading to a comprehensive analysis of the free boundary. More precisely, we show that near regular points of a coordinate function, the free boundary is analytic, whereas singular points lie on a smooth manifold. Additionally, we prove that uncoupled free boundary points are singular, indicating that regular points lie exclusively on the coupled free boundary. Furthermore, optimal regularity, non-degeneracy, and lower dimensional Hausdorff measure estimates are obtained. Explicit examples illustrate the sharpness of assumptions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_04863 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Interacting free boundaries in obstacle problems Araújo, Damião J. Teymurazyan, Rafayel Analysis of PDEs 35J47, 35R35, 60J60 We study obstacle problems governed by two distinct types of diffusion operators involving interacting free boundaries. We obtain a somewhat surprising coupling property, leading to a comprehensive analysis of the free boundary. More precisely, we show that near regular points of a coordinate function, the free boundary is analytic, whereas singular points lie on a smooth manifold. Additionally, we prove that uncoupled free boundary points are singular, indicating that regular points lie exclusively on the coupled free boundary. Furthermore, optimal regularity, non-degeneracy, and lower dimensional Hausdorff measure estimates are obtained. Explicit examples illustrate the sharpness of assumptions. |
| title | Interacting free boundaries in obstacle problems |
| topic | Analysis of PDEs 35J47, 35R35, 60J60 |
| url | https://arxiv.org/abs/2501.04863 |