On equicontinuity of mappings with inverse moduli inequalities by prime ends of variable domains

TL;DR

This paper investigates the boundary behavior of mappings satisfying inverse moduli inequalities, establishing conditions for their equicontinuity at prime ends of variable domains based on integrability of a majorant.

Contribution

It introduces conditions under which classes of mappings with inverse moduli inequalities are equicontinuous at prime ends, extending understanding of boundary behavior in variable domains.

Findings

Mappings are equicontinuous at prime ends if the majorant is integrable.

The study extends boundary behavior analysis to mappings with inverse moduli inequalities.

Conditions for equicontinuity depend on integrability of the majorant in the modulus inequality.

Abstract

The paper is devoted to the study of the boundary behavior of mappings. We consider mappings that satisfy inverse moduli inequalities of Poletskii type, under which the images of the domain under the mappings may change. It is proved that a classes of such mappings are equicontinuous with respect to prime ends of some domain if the majorant in the indicated modulus inequality is integrable.