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On the removal of singularities of the Orlicz–Sobolev classes

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Abstract

We study the local behavior of closed-open discrete mappings of the Orlicz–Sobolev classes in ℝn ; n ≥ 3: It is proved that the indicated mappings have continuous extensions to an isolated boundary point x 0 of a domain D/{x 0}, whenever its inner dilatation of order p ∈ (n − 1; n] has FMO (finite mean oscillation) at this point, and, in addition, the limit sets of f at x 0 and on ∂D are disjoint. Another sufficient condition for the possibility of a continuous extension can be formulated as a condition of divergence of a certain integral.

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Author information

Authors and Affiliations

  1. Zhytomyr Ivan Franko State University, Zhytomyr, Ukraine

    Evgeny A. Sevost’yanov

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

    Ruslan R. Salimov

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

    Evgenii A. Petrov

Authors
  1. Evgeny A. Sevost’yanov
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  2. Ruslan R. Salimov
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  3. Evgenii A. Petrov
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Corresponding author

Correspondence to Evgeny A. Sevost’yanov.

Additional information

Translated from Ukrains’kiĭ Matematychnyĭ Visnyk, Vol. 13, No. 3, pp. 324–349 July–September, 2016.

Translated from Russian by V.V. Kukhtin

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Sevost’yanov, E.A., Salimov, R.R. & Petrov, E.A. On the removal of singularities of the Orlicz–Sobolev classes. J Math Sci 222, 723–740 (2017). https://doi.org/10.1007/s10958-017-3327-2

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  • DOI: https://doi.org/10.1007/s10958-017-3327-2

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