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arXiv · 2403.03094

Refined geometric characterizations of weak $p$-quasiconformal mappings

Ruslan Salimov·Alexander Ukhlov
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Abstract

In this paper we consider refined geometric characterizations of weak $p$-quasiconformal mappings $\varphi:\Omega\to\widetilde{\Omega}$, where $\Omega$ and $\widetilde{\Omega}$ are domains in $\mathbb R^n$. We prove that mappings with the bounded on the set $\Omega\setminus S$, where a set $S$ has $\sigma$-finite $(n-1)$-measure, geometric $p$-dilatation, are $W^1_{p,\loc}$-- mappings and generate bounded composition operators on Sobolev spaces.

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Ruslan Salimov, Alexander Ukhlov. 2024-03-05. Refined geometric characterizations of weak $p$-quasiconformal mappings. https://arxiv.org/abs/2403.03094

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