arXiv subjects

E. A. Petrov

Publications and source records attributed to E. A. Petrov.

2 recordsLinked to original sources

arXiv2016

On removability of isolated singularities of classes Orlicz - Sobolev

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.

math.CV↗

arXiv2016

On equicontinuity of Sobolev classes in domains with locally connected boundary

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.

math.CV↗