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arXiv · 1601.03762

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

Evgeny Sevost'yanov
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Abstract

A boundary behavior of closed open discrete mappings of Sobolev and Orlicz--Sobolev classes in ${\Bbb R}^n,$ $n\ge 3,$ 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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Evgeny Sevost'yanov. 2016-02-12. On boundary behavior of mappings of Sobolev and Orlicz--Sobolev class. https://arxiv.org/abs/1601.03762

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