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arXiv · 1509.00887

On removability of isolated singularities of classes Orlicz - Sobolev

E. A. Petrov·R. R. Salimov·E. A. Sevost'yanov
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Abstract

We study the local behavior of the closed-open discrete maps of Orlich--Sobolev classes in ${\Bbb R}^n,$ $n\geqslant 3.$ It was found that these mappings $f$ have continuous extension in isolated point $x_0$ in $D\setminus\{x_0 \},$ as soon as their dilatation of order $p\in (n-1, n] $ has the majorant of class $FMO$ at said point, and moreover, limits set of mapping $f$ at $x_0$ and $\partial D$ are disjoint.

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E. A. Petrov, R. R. Salimov, E. A. Sevost'yanov. 2016-07-03. On removability of isolated singularities of classes Orlicz - Sobolev. https://arxiv.org/abs/1509.00887

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