Harmonic quasiconformal mappings between $\mathscr{C}^1$ smooth Jordan domains

David Kalaj

Harmonic quasiconformal mappings between $\mathscr{C}^1$ smooth Jordan domains

Complex Variables 2023-11-21 v2

Authors: David Kalaj

Abstract

We prove the following result. If $f$ is a harmonic quasiconformal mapping between two Jordan domains $D$ and $\Omega$ having $\mathscr{C}^1$ boundaries, then the function $f$ is globally H\"older continuous for every $\alpha<1$ but it is not Lipschitz in general. This extends and improves a classical theorem of S. Warschawski for conformal mappings.

Keywords

harmonic quasiconformal mappings jordan domains holder continuity lipschitz continuity conformal mappings

Cite

@article{arxiv.2003.03665,
  title  = {Harmonic quasiconformal mappings between $\mathscr{C}^1$ smooth Jordan domains},
  author = {David Kalaj},
  journal= {arXiv preprint arXiv:2003.03665},
  year   = {2023}
}

Comments

17 pages, this version contains the corrected paper as it was described in the erratum: Rev. Mat. Iberoam. 38, No. 1, 353-354 (2022)

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