Quasiconformal maps with controlled Laplacian

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http://hdl.handle.net/10138/312568

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Kalaj , D & Saksman , E 2019 , ' Quasiconformal maps with controlled Laplacian ' , Journal d'Analyse Mathematique , vol. 137 , no. 1 , pp. 251-268 . https://doi.org/10.1007/s11854-018-0072-5

Title: Quasiconformal maps with controlled Laplacian
Author: Kalaj, David; Saksman, Eero
Contributor: University of Helsinki, Department of Mathematics and Statistics
Date: 2019-03
Language: eng
Number of pages: 18
Belongs to series: Journal d'Analyse Mathematique
ISSN: 0021-7670
URI: http://hdl.handle.net/10138/312568
Abstract: We establish that every K-quasiconformal mapping w of the unit disk D onto a C-2-Jordan domain is Lipschitz provided that w L-p(D) for some p > 2. We also prove that if in this situation K 1 with ||w||L-p(D) 0, and D in C-1,C--sense with > 1/2, then the bound for the Lipschitz constant tends to 1. In addition, we provide a quasiconformal analogue of the Smirnov theorem on absolute continuity over the boundary.
Subject: 111 Mathematics
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