About one modulus inequality of the V\"ais\"al\"a Type

TL;DR

This paper extends the V"ais"al"a inequality to more general space mappings that are open, discrete, and differentiable almost everywhere, broadening its applicability beyond quasiregular mappings.

Contribution

It proves an analogue of the V"ais"al"a inequality for a wider class of space mappings with specific properties.

Findings

Established V"ais"al"a inequality analogue for general space mappings

Extended applicability beyond quasiregular mappings

Provided conditions under which the inequality holds

Abstract

The present paper is devoted to the study of space mappings, which are more general than quasiregular. The analogue of the known V\"ais\"al\"a inequality for the special types of curves was proved for the open, discrete, differentiable a.e. mappings having $N,$ $N^{-1}$ and $ACP^{-1}$ properties.