On the removal of singularities of the Orlicz–Sobolev classes

详细

We study the local behavior of closed-open discrete mappings of the Orlicz–Sobolev classes in ℝⁿ; n ≥ 3: It is proved that the indicated mappings have continuous extensions to an isolated boundary point x₀ of a domain D/{x₀}, whenever its inner dilatation of order p ∈ (n − 1; n] has FMO (finite mean oscillation) at this point, and, in addition, the limit sets of f at x₀ and on ∂D are disjoint. Another sufficient condition for the possibility of a continuous extension can be formulated as a condition of divergence of a certain integral.