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On the HÖlder property of mappings in domains and on boundaries

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Abstract

We study homeomorphisms and mappings with branching in domains of the Euclidean space. We establish pointwise HÖlder and Lipschitz properties of mappings whose characteristics satisfy a Dini-type condition or whose mean values over infinitesimal balls are finite at the corresponding points. Moreover, we find conditions on the complex coefficients of the Beltrami equations in the unit disk under which their homeomorphic solutions are HÖlder-continuous on the boundary.

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Authors and Affiliations

  1. Institute of Applied Mathematics and Mechanics of the NAS of Ukraine, Slavyansk, Ukraine

    Vladimir I. Ryazanov & Evgenii A. Sevost’yanov

  2. Laboratory of Mathematical Physics, Cherkassy National University, Cherkassy, Ukraine

    Vladimir I. Ryazanov

  3. Institute of Mathematics of the NAS of Ukraine, Kiev, Ukraine

    Ruslan R. Salimov

  4. I. Franko Zhitomir State University, Zhitomir, Ukraine

    Evgenii A. Sevost’yanov

Authors
  1. Vladimir I. Ryazanov
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  2. Ruslan R. Salimov
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  3. Evgenii A. Sevost’yanov
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Correspondence to Vladimir I. Ryazanov.

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Dedicated to the 100th anniversary of the birthday of Georgy Dmitrievich Suvorov

Translated from Ukrains’kiĭ Matematychnyĭ Visnyk, Vol. 16, No. 3, pp. 383–402 July–September, 2019.

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Ryazanov, V.I., Salimov, R.R. & Sevost’yanov, E.A. On the HÖlder property of mappings in domains and on boundaries. J Math Sci 246, 60–74 (2020). https://doi.org/10.1007/s10958-020-04723-2

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  • DOI: https://doi.org/10.1007/s10958-020-04723-2

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