On equicontinuity of Sobolev classes in domains with locally connected boundary

2016/03/12 by E. A. Petrov, Petrov, E. A., E. A. Sevost'yanov +1
Mathematics · #30C65 #Complex Variables (math.CV) #FOS: Mathematics #math.CV #msc:30C65

paper · pdf · doi:10.48550/arxiv.1603.03885

in Russian

arxiv created 2016/03/12 · arxiv updated 2016/03/15

Abstract

A behavior of homeomorphisms of Orlicz classes in a closure of a domain is investigated. It is proved that above classes are equicontinuous in the closure of domains with some restrictions on it's boundaries provided that the corresponding inner dilatation of order p has a majorant of finite mean oscillation at every point.

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