Journal d'Analyse Mathématique

, Volume 137, Issue 1, pp 251–268 | Cite as

Quasiconformal maps with controlled Laplacian

  • David KalajEmail author
  • Eero Saksman


We establish that every K-quasiconformal mapping w of the unit disk \(\mathbb{D}\) onto a C2-Jordan domain Ω is Lipschitz provided that ΔwLp(\(\mathbb{D}\)) for some p > 2. We also prove that if in this situation K → 1 with ||Δw||Lp(\(\mathbb{D}\)) → 0, and Ω→\(\mathbb{D}\) in C1,α-sense with α > 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.


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© The Hebrew University of Jerusalem 2019

Authors and Affiliations

  1. 1.University of Montenegro Faculty of Natural Sciences and MathematicsPodgoricaMontenegro
  2. 2.Department Of Mathematics and StatisticsUniversity of HelsinkiHelsinkiFinland

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