On equicontinuity of Sobolev classes in domains with locally connected boundary

E. A. Petrov; E. A. Sevost'yanov

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arXiv · 1603.03885

On equicontinuity of Sobolev classes in domains with locally connected boundary

E. A. Petrov·E. A. Sevost'yanov

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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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E. A. Petrov, E. A. Sevost'yanov. 2016-03-12. On equicontinuity of Sobolev classes in domains with locally connected boundary. https://arxiv.org/abs/1603.03885

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