Israel Journal of Mathematics

, Volume 220, Issue 1, pp 453–478 | Cite as

On the Lipschitz continuity of certain quasiregular mappings between smooth Jordan domains

  • Jiaolong Chen
  • Peijin Li
  • Swadesh Kumar Sahoo
  • Xiantao Wang
Article

Abstract

We first investigate the Lipschitz continuity of (K,K’)-quasiregular C2 mappings between two Jordan domains with smooth boundaries, satisfying certain partial differential inequalities concerning Laplacian. Then two applications of the obtained result are given: As a direct consequence, we get the Lipschitz continuity of ρ-harmonic (K,K’)-quasiregular mappings, and as the other application, we study the Lipschitz continuity of (K,K’)- quasiconformal self-mappings of the unit disk, which are the solutions of the Poisson equation Δw = g. These results generalize and extend several recently obtained results by Kalaj, Mateljević and Pavlović.

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Copyright information

© Hebrew University of Jerusalem 2017

Authors and Affiliations

  • Jiaolong Chen
    • 1
  • Peijin Li
    • 2
  • Swadesh Kumar Sahoo
    • 3
  • Xiantao Wang
    • 1
  1. 1.Department of MathematicsShantou University ShantouGuangdongPeople’s Republic of China
  2. 2.Department of MathematicsHunan Normal University ChangshaHunanPeople’s Republic of China
  3. 3.Discipline of MathematicsIndian Institute of Technology IndoreSimrol, IndoreIndia

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