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arXiv · 2108.10375

On the inverse $K_I$-inequality for one class of mappings

Oleksandr Dovhopiatyi·Evgeny Sevost'yanov
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Abstract

We study mappings differentiable almost everywhere, possessing the $N$-Luzin property, the $ N^{\,-1}$-property on the spheres with respect to the $(n-1)$-dimensional Hausdorff measure and such that the image of the set where its Jacobian equals to zero has a zero Lebesgue measure. It is proved that such mappings satisfy the lower bound for the Poletsky-type distortion in their domain of definition.

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Oleksandr Dovhopiatyi, Evgeny Sevost'yanov. 2021-08-23. On the inverse $K_I$-inequality for one class of mappings. https://arxiv.org/abs/2108.10375

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