2017
Том 69
№ 9

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

Sevost'yanov E. A.

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.

Citation Example: Sevost'yanov E. A. On the removability of isolated singularities of Orlicz – Sobolev classes with branching // Ukr. Mat. Zh. - 2016. - 68, № 5. - pp. 683-693.