Mappings of finite distortion : boundary extensions in uniform domains
Äkkinen, T., & Guo, C.-Y. (2017). Mappings of finite distortion : boundary extensions in uniform domains. Annali di Matematica Pura ed Applicata, 196 (1), 65-83. doi:10.1007/s10231-016-0563-x
Published inAnnali di Matematica Pura ed Applicata
© Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag Berlin Heidelberg 2016. This is a final draft version of an article whose final and definitive form has been published by Springer. Published in this repository with the kind permission of the publisher.
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.