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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2506.22042 |
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| _version_ | 1866914148935270400 |
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| author | Campbell, Daniel |
| author_facet | Campbell, Daniel |
| contents | In this paper we give an elementary proof that sets of zero $p,1$-Sobolev-Lorentz capacity are $\mathcal{H}^{n-p}$-null sets independently of non-linear potential theory. We further show that there exists a set of Sobolev-Lorentz-$(p,1)$ capacity equal zero with Hausdorff dimension equal $n-p$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_22042 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A note on Sobolev-Lorentz Capacity and Hausdorff measure Campbell, Daniel Analysis of PDEs In this paper we give an elementary proof that sets of zero $p,1$-Sobolev-Lorentz capacity are $\mathcal{H}^{n-p}$-null sets independently of non-linear potential theory. We further show that there exists a set of Sobolev-Lorentz-$(p,1)$ capacity equal zero with Hausdorff dimension equal $n-p$. |
| title | A note on Sobolev-Lorentz Capacity and Hausdorff measure |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2506.22042 |