On boundary H\"{o}lder logarithmic continuity of mappings in some domains

TL;DR

This paper investigates the boundary regularity of certain mappings with controlled distortion, proving they exhibit logarithmic Hölder continuity at boundary points under specific domain conditions.

Contribution

It establishes boundary logarithmic Hölder continuity for mappings with modulus distortion estimates in particular domain settings, extending regularity results.

Findings

Mappings are logarithmic Hölder continuous at boundary points.

Continuity depends on domain conditions and distortion estimates.

Results apply to a class of mappings with controlled modulus distortion.

Abstract

We study mappings satisfying some estimate of distortion of modulus of families of paths. Under some conditions on definition and mapped domains, we have proved that these mappings are logarithmic H\"{o}lder continuous at boundary points.