Mappings of finite distortion: boundary extensions in uniform domains

TL;DR

This paper proves that mappings with finite distortion in uniform domains can be extended to the boundary with preserved exponential integrability, generalizing previous results on analytic and bounded distortion mappings.

Contribution

It extends boundary extension results to mappings with exponentially integrable distortion in uniform domains, providing quantitative bounds on the extensions.

Findings

Mappings with exponentially integrable distortion extend to the boundary

Extensions are exponentially integrable with bounds

Generalizes previous boundary extension results

Abstract

In this paper, we consider mappings on uniform domains with exponentially integrable distortion whose Jacobian determinants are integrable. We show that such mappings can be extended to the boundary and moreover these extensions are exponentially integrable with quantitative bounds. This extends previous results of Chang and Marshall on analytic functions, Poggi-Corradini and Rajala and Akkinen and Rajala on mappings of bounded and finite distortion.