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arXiv · 2211.12802

Finely quasiconformal mappings

Panu Lahti
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Abstract

We introduce a relaxed version of the metric definition of quasiconformality that is natural also for mappings of low regularity, including $W_{\mathrm{loc}}^{1,1}(\mathbb{R}^n;\mathbb{R}^n)$-mappings. Then we show on the plane that this relaxed definition can be used to prove Sobolev regularity, and that these ``finely quasiconformal'' mappings are in fact quasiconformal.

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Panu Lahti. 2024-06-05. Finely quasiconformal mappings. https://doi.org/10.1017/prm.2024.135

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