On removability of isolated singularities of Orlicz-Sobolev classes with branching

TL;DR

This paper investigates the conditions under which certain Orlicz-Sobolev mappings can be continuously extended to isolated boundary points, focusing on the role of inner dilatation's finite mean oscillation and integral divergence.

Contribution

It establishes new criteria for the removability of isolated singularities of Orlicz-Sobolev mappings with branching, involving finite mean oscillation and integral divergence conditions.

Findings

Mappings extend continuously if inner dilatation has FMO at the boundary point.

Disjointness of limit sets at the boundary point and the domain boundary is crucial.

Integral divergence provides an alternative sufficient condition for extension.

Abstract

A local behavior of closed open discrete mappings of Orlicz--Sobolev classes in ${\Bbb R}^n,$ $n\ge 3,$ is studied. It is proved that, mappings mentioned above have continuous extension to isolated boundary point $x_0$ of a domain $D\setminus\{x_0\}$ whenever $n-1$ degree of its inner dilatation has $FMO$ (finite mean oscillation) at the point and, besides that, limit sets of $f$ at $x_0$ and $\partial D$ are disjoint. Another sufficient condition of possibility of continuous extension is a divergence of some integral