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| Format: | Preprint |
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2023
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| Online Access: | https://arxiv.org/abs/2307.07590 |
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| _version_ | 1866909644144771072 |
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| author | Hernández, Joan |
| author_facet | Hernández, Joan |
| contents | In the present paper we characterize the $(1/2,+)$-caloric capacity (associated with the $1/2$-fractional heat equation) of the usual corner-like Cantor set of $\mathbb{R}^{n+1}$. The results obtained for the latter are analogous to those found for Newtonian capacity. Moreover, we also characterize the BMO and $\text{Lip}_α$ variants ($0<α<1$) of the $1/2$-caloric capacity in terms of the Hausdorff contents $\mathcal{H}^n_\infty$ and $\mathcal{H}^{n+α}_\infty$ respectively. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_07590 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the $(1/2,+)$-caloric capacity of Cantor sets Hernández, Joan Analysis of PDEs Classical Analysis and ODEs In the present paper we characterize the $(1/2,+)$-caloric capacity (associated with the $1/2$-fractional heat equation) of the usual corner-like Cantor set of $\mathbb{R}^{n+1}$. The results obtained for the latter are analogous to those found for Newtonian capacity. Moreover, we also characterize the BMO and $\text{Lip}_α$ variants ($0<α<1$) of the $1/2$-caloric capacity in terms of the Hausdorff contents $\mathcal{H}^n_\infty$ and $\mathcal{H}^{n+α}_\infty$ respectively. |
| title | On the $(1/2,+)$-caloric capacity of Cantor sets |
| topic | Analysis of PDEs Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2307.07590 |