JournalsrmiVol. 38, No. 1pp. 95–111

Harmonic quasiconformal mappings between C1\mathcal{C}^1 smooth Jordan domains

  • David Kalaj

    University of Montenegro, Podgorica, Montenegro
Harmonic quasiconformal mappings between $\mathcal{C}^1$ smooth Jordan domains cover
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Abstract

We prove the following result. If ff is a harmonic quasiconformal mapping between two Jordan domains DD and Ω\Omega having C1\mathcal{C}^1 boundaries, then the function ff is globally Hölder continuous for every α<1\alpha<1 but it is not necessarily Lipschitz in general. This result extends and improves a classical theorem of S. Warschawski for conformal mappings.

Cite this article

David Kalaj, Harmonic quasiconformal mappings between C1\mathcal{C}^1 smooth Jordan domains. Rev. Mat. Iberoam. 38 (2022), no. 1, pp. 95–111

DOI 10.4171/RMI/1272