On behavior of a class of mappings in terms of prime ends

TL;DR

This paper investigates the boundary behavior of a class of finite distortion mappings using prime ends, establishing conditions for equicontinuity at the boundary based on integrability of a distortion function.

Contribution

It provides new results on boundary behavior of mappings with finite distortion satisfying Poletsky inequality, linking integrability conditions to equicontinuity at boundary points.

Findings

Mappings are equicontinuous at boundary points under certain integrability conditions.

Boundary behavior analyzed using prime ends for mappings with finite distortion.

Results extend understanding of boundary regularity in geometric function theory.

Abstract

The paper is devoted to the study of mappings with finite distortion, actively studied recently. For mappings whose inverse satisfy the Poletsky inequality, the results on boundary behavior in terms of prime ends are obtained. In particular, it was proved that the families of the indicated mappings are equicontinuous at the points of the boundary if a certain function determining the distortion of the module under the mappings is integrable in a given domain.