On behavior of one class of mappings acting onto domains with a locally quasiconformal boundary

TL;DR

This paper investigates the behavior of certain mappings satisfying the inverse Poletsky inequality, establishing their local Hölder logarithmic continuity near boundary points in complex domains with locally quasiconformal boundaries.

Contribution

It introduces new regularity results for mappings with inverse Poletsky inequality acting on complex domains with locally quasiconformal boundaries.

Findings

Mappings exhibit Hölder logarithmic continuity near boundary points.

Results apply to domains with locally quasiconformal boundaries and prime end regularity.

Provides new insights into boundary behavior of inverse Poletsky inequality mappings.

Abstract

The article is devoted to the study of mappings that satisfy the so-called inverse Poletsky inequality. We consider mappings of quasiextremal distance domains, domains with a locally quasiconformal boundary, and domains which are regular in the sense of prime ends onto domains with a locally quasiconformal boundary, regular domains, or domains which are locally H\"{o}lder equivalent to a half-ball on its boundary. For such mappings, we have obtained the H\"{o}lder logarithmic continuity in some neighborhood of its boundary points.