On the boundary behavior of weak $(p,q)$-quasiconformal mappings

TL;DR

This paper investigates how weak $(p,q)$-quasiconformal mappings behave at the boundaries of domains in Euclidean space, using capacitary distortion properties to analyze their boundary behavior.

Contribution

It introduces a method based on capacitary distortion to study boundary behavior of weak $(p,q)$-quasiconformal mappings, extending understanding of their boundary properties.

Findings

Boundary behavior characterized for weak $(p,q)$-quasiconformal mappings.

Capacitary distortion properties are key to understanding boundary limits.

Results apply to domains in Euclidean space with specific $p,q$ ranges.

Abstract

Let $\Omega$ and $\widetilde{\Omega}$ be domains in the Euclidean space $\mathbb R^n$. We study the boundary behavior of weak $(p,q)$-quasiconformal mappings, $\varphi:\Omega\to \widetilde{\Omega}$, $n-1<q\leq p<n$. The suggested method is based on the capacitary distortion properties of the weak $(p,q)$-quasiconformal mappings.