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Absolute continuity on paths of spatial open discrete mappings

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We prove that open discrete mappings of Sobolev classes \(W_\mathrm{loc}^{1, p},\) \(p>n-1,\) with locally integrable inner dilatations admit \(ACP_p^{\,-1}\)-property, which means that these mappings are absolutely continuous on almost all preimage paths with respect to p-module. In particular, our results extend the well-known Poletskiĭ lemma for quasiregular mappings. We also establish the upper bounds for p-module of such mappings in terms of integrals depending on the inner dilatations and arbitrary admissible functions.

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Authors and Affiliations

  1. Department of Applied Mathematics, Holon Institute of Technology, Holon, 5810201, Israel

    Anatoly Golberg

  2. Department of Mathematical Analysis, Zhitomyr State University, Zhitomyr, 10 008, Ukraine

    Evgeny Sevost’yanov

Authors
  1. Anatoly Golberg
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  2. Evgeny Sevost’yanov
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Correspondence to Anatoly Golberg.

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Golberg, A., Sevost’yanov, E. Absolute continuity on paths of spatial open discrete mappings. Anal.Math.Phys. 8, 25–35 (2018). https://doi.org/10.1007/s13324-016-0159-z

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