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arXiv · 2003.03665

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

David Kalaj
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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.

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David Kalaj. 2020-03-07. Harmonic quasiconformal mappings between $\mathscr{C}^1$ smooth Jordan domains. https://arxiv.org/abs/2003.03665

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