On the boundary behavior of some classes of mappings

E. A. Sevost'yanov

Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 46, Tome 467 (2018), pp. 169-190

Résumé

The boundary behavior of closed open discrete mappings of Sobolev and Orlicz–Sobolev classes in $\mathbb R^n$, $n\ge3$, is studied. It is proved that a mapping $f$ mentioned above has a continuous extension to a boundary point $x_0\in\partial D$ of a domain $D\subset\mathbb R^n$ whenever its inner dilatation of order $\alpha>n-1$ has a majorant of finite mean oscillation class at the point in question. Another sufficient condition for continuous extension of mappings is the divergence of some integral. Some results on continuous extension of these mappings to an isolated boundary point are also proved.