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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.19252 |
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| _version_ | 1866917163481169920 |
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| author | Creo, Simone Fragapane, Salvatore |
| author_facet | Creo, Simone Fragapane, Salvatore |
| contents | We study obstacle problems for the regional fractional $p$-Laplacian in a domain $Ω\subset\mathbb{R}^2$ having as fractal boundary the Koch snowflake. We prove well-posedness results for the solution of the obstacle problem, as well as two equivalent formulations. Moreover, we study corresponding approximating obstacle problems in a sequence of domains $Ω_n\subset\mathbb{R}^2$ having as boundary the $n$-th pre-fractal approximation of the Koch snowflake, for $n\in\mathbb{N}$. After proving the well-posedness of the approximating obstacle problems, we perform the asymptotic analysis for both $n\to+\infty$ and $p\to+\infty$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_19252 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Obstacle problems for the fractional $p$-Laplacian on fractal domains: well-posedness and asymptotics Creo, Simone Fragapane, Salvatore Analysis of PDEs We study obstacle problems for the regional fractional $p$-Laplacian in a domain $Ω\subset\mathbb{R}^2$ having as fractal boundary the Koch snowflake. We prove well-posedness results for the solution of the obstacle problem, as well as two equivalent formulations. Moreover, we study corresponding approximating obstacle problems in a sequence of domains $Ω_n\subset\mathbb{R}^2$ having as boundary the $n$-th pre-fractal approximation of the Koch snowflake, for $n\in\mathbb{N}$. After proving the well-posedness of the approximating obstacle problems, we perform the asymptotic analysis for both $n\to+\infty$ and $p\to+\infty$. |
| title | Obstacle problems for the fractional $p$-Laplacian on fractal domains: well-posedness and asymptotics |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2512.19252 |