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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2403.03094 |
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| _version_ | 1866910354335858688 |
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| author | Salimov, Ruslan Ukhlov, Alexander |
| author_facet | Salimov, Ruslan Ukhlov, Alexander |
| contents | In this paper we consider refined geometric characterizations of weak $p$-quasiconformal mappings $φ:Ω\to\widetildeΩ$, where $Ω$ and $\widetildeΩ$ are domains in $\mathbb R^n$. We prove that mappings with the bounded on the set $Ω\setminus S$, where a set $S$ has $σ$-finite $(n-1)$-measure, geometric $p$-dilatation, are $W^1_{p,\loc}$-- mappings and generate bounded composition operators on Sobolev spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_03094 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Refined geometric characterizations of weak $p$-quasiconformal mappings Salimov, Ruslan Ukhlov, Alexander Analysis of PDEs 46E35, 30C65 In this paper we consider refined geometric characterizations of weak $p$-quasiconformal mappings $φ:Ω\to\widetildeΩ$, where $Ω$ and $\widetildeΩ$ are domains in $\mathbb R^n$. We prove that mappings with the bounded on the set $Ω\setminus S$, where a set $S$ has $σ$-finite $(n-1)$-measure, geometric $p$-dilatation, are $W^1_{p,\loc}$-- mappings and generate bounded composition operators on Sobolev spaces. |
| title | Refined geometric characterizations of weak $p$-quasiconformal mappings |
| topic | Analysis of PDEs 46E35, 30C65 |
| url | https://arxiv.org/abs/2403.03094 |