Dimension of the singular set in the parabolic obstacle problem
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866915839659212800 |
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| author | Martínez, Alejandro Ros-Oton, Xavier |
| author_facet | Martínez, Alejandro Ros-Oton, Xavier |
| contents | In this paper we study the singular set in the parabolic obstacle problem for general obstacles $φ\in C^{2,1}$. We prove that the singular set has parabolic Hausdorff dimension at most $n-1$. Prior to our result, this was only known when $Δφ\equiv -1$. Our approach combines a truncated parabolic frequency formula and monotonicity estimates with an iterative argument showing that the frequency is saturated for all values of the truncation parameter between $2$ and $3$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_06352 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Dimension of the singular set in the parabolic obstacle problem Martínez, Alejandro Ros-Oton, Xavier Analysis of PDEs 35R35, 35B65, 35K10 In this paper we study the singular set in the parabolic obstacle problem for general obstacles $φ\in C^{2,1}$. We prove that the singular set has parabolic Hausdorff dimension at most $n-1$. Prior to our result, this was only known when $Δφ\equiv -1$. Our approach combines a truncated parabolic frequency formula and monotonicity estimates with an iterative argument showing that the frequency is saturated for all values of the truncation parameter between $2$ and $3$. |
| title | Dimension of the singular set in the parabolic obstacle problem |
| topic | Analysis of PDEs 35R35, 35B65, 35K10 |
| url | https://arxiv.org/abs/2603.06352 |