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

2016/01/14 by Evgeny Sevost'yanov, Sevost'yanov, Evgeny
Mathematics · #30C65 #Complex Variables (math.CV) #FOS: Mathematics #math.CV #msc:30C65

paper · pdf · doi:10.48550/arxiv.1601.03762

in Russian

arxiv created 2016/02/12 · arxiv updated 2016/02/15

Abstract

A boundary behavior of closed open discrete mappings of Sobolev and Orlicz--Sobolev classes in \Bbb Rⁿ, n≥ 3, is studied. It is proved that, mappings mentioned above have a continuous extension to boundary point x₀ 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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