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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2409.16066 |
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| _version_ | 1866916408988794880 |
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| author | Moring, Kristian Scheven, Christoph |
| author_facet | Moring, Kristian Scheven, Christoph |
| contents | We consider different notions of capacity related to the parabolic $p$-Laplace equation. Our focus is on a variational notion, which is consistent in the full range $1<p<\infty$. For such a notion we show some basic properties as well as its connection to other notions of capacity presented in the literature, and to a certain parabolic version of the Hausdorff measure. As applications, we use the introduced variational notion of capacity to study polar sets and removability results for supersolutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_16066 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On notions of $p$-parabolic capacity and applications Moring, Kristian Scheven, Christoph Analysis of PDEs 35K55, 35K92, 31C15, 31C45 We consider different notions of capacity related to the parabolic $p$-Laplace equation. Our focus is on a variational notion, which is consistent in the full range $1<p<\infty$. For such a notion we show some basic properties as well as its connection to other notions of capacity presented in the literature, and to a certain parabolic version of the Hausdorff measure. As applications, we use the introduced variational notion of capacity to study polar sets and removability results for supersolutions. |
| title | On notions of $p$-parabolic capacity and applications |
| topic | Analysis of PDEs 35K55, 35K92, 31C15, 31C45 |
| url | https://arxiv.org/abs/2409.16066 |