On the Removability of Isolated Singularities of Orlicz–Sobolev Classes with Branching

Abstract

We study the local behavior of closed-open discrete mappings of the Orlicz–Sobolev classes in $$ {\mathbb{R}}^n $$ , n ≥ 3. It is proved that the indicated mappings have continuous extensions to an isolated boundary point x 0 of a domain D {x 0}, whenever its inner dilatation has FMO (finite mean oscillation) at this point and, in addition, the limit sets of f at x 0 and on ∂D are disjoint. Another sufficient condition for the possibility of continuous extension can be formulated as a condition of divergence of a certain integral.