On removability of isolated singularities of classes Orlicz - Sobolev

TL;DR

This paper investigates the conditions under which certain Orlicz-Sobolev class mappings in higher dimensions can be continuously extended over isolated singularities, focusing on dilatation behavior and boundary limits.

Contribution

It establishes new criteria involving FMO majorants for the removability of isolated singularities in Orlicz-Sobolev mappings in -dimensional space.

Findings

Mappings with dilatation of order p in (n-1, n] have continuous extensions at isolated points.

Limits set of the mapping at the singularity and boundary are disjoint under certain conditions.

The results extend understanding of singularity removability in higher-dimensional Orlicz-Sobolev classes.

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.