On the removability of isolated singularities of Orlicz – Sobolev classes with branching

Abstract

The local behavior of closed-open discrete mappings of the Orlicz – Sobolev classes in $R^n,\; n \geq 3$, is investigated. It is proved that the indicated mappings have continuous extensions to an isolated boundary point $x_0$ of the domain $D \setminus \{ x0\}$, whenever the $n - 1$ degree of its inner dilatation has FMO (finite mean oscillation) at this point and, in addition, the limit sets of $f$ at $x_0$ and $\partial D$ are disjoint. Another sufficient condition for the possibility of continuous extension can be formulated as a condition of divergence of a certain integral.