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

Abstract

We prove the following result. If $f$ is a harmonic quasiconformal mapping between two Jordan domains $D$ and $\Omega$ having ${\mathcal{C}}^1$ boundaries, then the function $f$ is globally Hölder 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.

arXiv comment17 pages, this version contains the corrected paper as it was described in the erratum: Rev. Mat. Iberoam. 38, No. 1, 353-354 (2022)

Cited by in corpus (1)

• H$\ddot{\mathbf{o}}$lder continuity of QCH mappings from the unit ball to a domain with $C^1$ boundary