Harmonic quasiconformal mappings between \(\mathcal{C}^1\) smooth Jordan domains (Q832431)

Summary: 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 necessarily Lipschitz in general. This result extends and improves a classical theorem of S. Warschawski for conformal mappings.