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On the behavior of Orlicz–Sobolev mappings with branching on the unit sphere

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Abstract

We study the mappings of the Orlicz–Sobolev classes with a branching defined in the unit ball of the Euclidean space. We have obtained estimates for the distortion of the distance under these mappings at the points of the unit sphere. Under some conditions, we have also obtained the Hölder continuity of the mappings mentioned above. If we suppose that the considered mappings are solutions to certain Laplacian-gradient inequalities, we get the Lipschitz property. In section 7–9, we review some results, prove a new result, Theorem 7.1, and outline the proof of Theorem 9.2.

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Authors and Affiliations

  1. University of Belgrade, Faculty of Mathematics, Belgrade, Serbia

    Miodrag Mateljevic

  2. Zhytomyr Ivan Franko State University, Zhytomyr, Ukraine

    Evgeny Sevost’yanov

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

    Evgeny Sevost’yanov

Authors
  1. Miodrag Mateljevic
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  2. Evgeny Sevost’yanov
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Correspondence to Miodrag Mateljevic.

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Translated from Ukrains’kiĭ Matematychnyĭ Visnyk, Vol. 19, No. 4, pp. 541–583, October–December, 2022.

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Mateljevic, M., Sevost’yanov, E. On the behavior of Orlicz–Sobolev mappings with branching on the unit sphere. J Math Sci 270, 467–499 (2023). https://doi.org/10.1007/s10958-023-06358-5

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