Exponential integrability of mappings of finite distortion
Tuomo ÄkkinenUniversity of Jyväskylä, Finland
Kai RajalaUniversity of Jyväskylä, Finland
We consider mappings with exponentially integrable distortion whose Jacobian determinants are integrable over the -ball. We show that the boundary extensions of such mappings are exponentially integrable with bounds, and give examples to illustrate that there is not too much room for improvement. This extends the results of Beurling , and Chang and Marshall ,  on analytic functions, and Poggi-Corradini and Rajala  on quasiregular mappings.
Cite this article
Tuomo Äkkinen, Kai Rajala, Exponential integrability of mappings of finite distortion. Rev. Mat. Iberoam. 31 (2015), no. 4, pp. 1459–1476DOI 10.4171/RMI/876