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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2512.15277 |
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| _version_ | 1866915681637761024 |
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| author | Borowski, Michał Elenius, Theo Schätzler, Leah Stolnicki, David |
| author_facet | Borowski, Michał Elenius, Theo Schätzler, Leah Stolnicki, David |
| contents | We characterize removable sets for Hölder continuous solutions to degenerate parabolic equations of $p$-growth. A sufficient and necessary condition for a set to be removable is given in terms of an intrinsic parabolic Hausdorff measure, which depends on the considered Hölder exponent. We present a new method to prove the sufficient condition, which relies only on fundamental properties of the obstacle problem and supersolutions, and applies to a general class of operators. For the necessity of the condition, we establish the Hölder continuity of solutions with measure data, provided the measure satisfies a suitable decay property. The techniques developed in this article provide a new point of view even in the case $p=2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_15277 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Carleson-type removability for $p$-parabolic equations Borowski, Michał Elenius, Theo Schätzler, Leah Stolnicki, David Analysis of PDEs We characterize removable sets for Hölder continuous solutions to degenerate parabolic equations of $p$-growth. A sufficient and necessary condition for a set to be removable is given in terms of an intrinsic parabolic Hausdorff measure, which depends on the considered Hölder exponent. We present a new method to prove the sufficient condition, which relies only on fundamental properties of the obstacle problem and supersolutions, and applies to a general class of operators. For the necessity of the condition, we establish the Hölder continuity of solutions with measure data, provided the measure satisfies a suitable decay property. The techniques developed in this article provide a new point of view even in the case $p=2$. |
| title | Carleson-type removability for $p$-parabolic equations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2512.15277 |