On the removal of singularities of the Orlicz–Sobolev classes
- Authors: Sevost’yanov E.A.1, Salimov R.R.2, Petrov E.A.3
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Affiliations:
- Zhytomyr Ivan Franko State University
- Institute of Mathematics of the NAS of Ukraine
- Institute of Applied Mathematics and Mechanics of the NAS of Ukraine
- Issue: Vol 222, No 6 (2017)
- Pages: 723-740
- Section: Article
- URL: https://journal-vniispk.ru/1072-3374/article/view/239261
- DOI: https://doi.org/10.1007/s10958-017-3327-2
- ID: 239261
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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 x0 of a domain D/{x0}, 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 x0 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.
About the authors
Evgeny A. Sevost’yanov
Zhytomyr Ivan Franko State University
Author for correspondence.
Email: esevostyanov2009@mail.ru
Ukraine, Zhytomyr
Ruslan R. Salimov
Institute of Mathematics of the NAS of Ukraine
Email: esevostyanov2009@mail.ru
Ukraine, Kiev
Evgenii A. Petrov
Institute of Applied Mathematics and Mechanics of the NAS of Ukraine
Email: esevostyanov2009@mail.ru
Ukraine, Slavyansk
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