On removability of isolated singularities of classes Orlicz - Sobolev

Abstract

We study the local behavior of the closed-open discrete maps of Orlich--Sobolev classes in ${\mathbb{R}}^n,$ $n⩾3.$ It was found that these mappings $f$ have continuous extension in isolated point $x_0$ in $D\setminus \{x_0\},$ as soon as their dilatation of order $p\in (n-1,n]$ has the majorant of class $FMO$ at said point, and moreover, limits set of mapping $f$ at $x_0$ and $\partial D$ are disjoint.

arXiv comment21 pages, in Russian