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 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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