Revista Matemática Iberoamericana

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Volume 31, Issue 4, 2015, pp. 1459–1476
DOI: 10.4171/RMI/876

Published online: 2015-12-23

Exponential integrability of mappings of finite distortion

Tuomo Äkkinen[1] and Kai Rajala[2]

(1) University of Jyväskylä, Finland
(2) University of Jyväskylä, Finland

We consider mappings with exponentially integrable distortion whose Jacobian determinants are integrable over the $n$-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 [2], and Chang and Marshall [3], [10] on analytic functions, and Poggi-Corradini and Rajala [14] on quasiregular mappings.

Keywords: Mappings of finite distortion, exponential integrability, radial extension

Äkkinen Tuomo, Rajala Kai: Exponential integrability of mappings of finite distortion. Rev. Mat. Iberoam. 31 (2015), 1459-1476. doi: 10.4171/RMI/876