On boundary behavior of mappings of Sobolev and Orlicz--Sobolev class

Abstract

A boundary behavior of closed open discrete mappings of Sobolev and Orlicz--Sobolev classes in ${\mathbb{R}}^n,$ $n\ge 3,$ is studied. It is proved that, mappings mentioned above have a continuous extension to boundary point $x_0$ of a domain $D$ whenever its inner dilatation of order $p$ has a majorant $FMO$ (finite mean oscillation) at the point. Another sufficient condition of possibility of continuous extension is a divergence of some integral.

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