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The inverse Poletsky inequality in one class of mappings

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Abstract

Almost everywhere differentiable mappings possessing the Luzin N-property, the N–1-property on spheres with respect to the (n–1)-dimensional Hausdorff measure, and the zero Lebesgue measure of the image of points where their Jacobian vanishes, have been studied. It has been proved that such mappings satisfy the lower estimate of the Poletsky-type distortion in their domain. In particular, if homeomorphism has an inverse from the Orlicz–Sobolev class, then, provided the Calderón condition for the determining function holds, it satisfies the inverse Poletsky inequality.

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Authors and Affiliations

  1. Zhytomyr Ivan Franko State University, Zhytomyr, Ukraine

    Evgeny O. Sevost’yanov

  2. Institute of Applied Mathematics and Mechanics of the NAS of Ukraine, Slov’yans’k, Ukraine

    Evgeny O. Sevost’yanov

Authors
  1. Evgeny O. Sevost’yanov
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Correspondence to Evgeny O. Sevost’yanov.

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Translated from Ukrains’kiĭ Matematychnyĭ Visnyk, Vol. 19, No. 2, pp. 254–274, April–June, 2022.

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Sevost’yanov, E.O. The inverse Poletsky inequality in one class of mappings. J Math Sci 264, 455–470 (2022). https://doi.org/10.1007/s10958-022-06011-7

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  • DOI: https://doi.org/10.1007/s10958-022-06011-7

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