On the Boundary Behavior of Some Classes of Mappings

Abstract

We study the boundary behavior of closed open discrete mappings from the Sobolev and Orlicz–Sobolev classes in ℝⁿ, n ≥ 3. It is proved that such a mapping f can be extended by continuity to a boundary point x₀ ∈ ∂ D of a domain D ⊂ ℝⁿ whenever its inner dilatation of order α > n− 1 has a majorant from the finite mean oscillation class at the point in question. Another sufficient condition for the existence of a continuous extension is the divergence of some integral. We also prove some results on the continuous extension of such a mapping to an isolated boundary point.