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

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Abstract

We first investigate the Lipschitz continuity of (K,K’)-quasiregular C 2 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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Authors and Affiliations

  1. Department of Mathematics, Shantou University Shantou, Guangdong, 515063, People’s Republic of China

    Jiaolong Chen & Xiantao Wang

  2. Department of Mathematics, Hunan Normal University Changsha, Hunan, 410081, People’s Republic of China

    Peijin Li

  3. Discipline of Mathematics, Indian Institute of Technology Indore, Simrol, Indore, 453 552, India

    Swadesh Kumar Sahoo

Authors
  1. Jiaolong Chen
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  2. Peijin Li
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  3. Swadesh Kumar Sahoo
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  4. Xiantao Wang
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Correspondence to Xiantao Wang.

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Chen, J., Li, P., Sahoo, S.K. et al. On the Lipschitz continuity of certain quasiregular mappings between smooth Jordan domains. Isr. J. Math. 220, 453–478 (2017). https://doi.org/10.1007/s11856-017-1522-y

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  • DOI: https://doi.org/10.1007/s11856-017-1522-y

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