On removability of isolated singularities of Orlicz-Sobolev classes with branching

Abstract

A local behavior of closed open discrete mappings of Orlicz--Sobolev classes in ${\Bbb R}^n,$ $n\ge 3,$ is studied. It is proved that, mappings mentioned above have continuous extension to isolated boundary point $x_0$ of a domain $D\setminus\{x_0\}$ whenever $n-1$ degree of its inner dilatation has $FMO$ (finite mean oscillation) at the point and, besides that, limit sets of $f$ at $x_0$ and $\partial D$ are disjoint. Another sufficient condition of possibility of continuous extension is a divergence of some integral