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We prove the following result. If is a harmonic quasiconformal mapping between two Jordan domains and having boundaries, then the function is globally Hölder continuous for every but it is not necessarily Lipschitz in general. This result extends and improves a classical theorem of S. Warschawski for conformal mappings.
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David Kalaj, Harmonic quasiconformal mappings between smooth Jordan domains. Rev. Mat. Iberoam. 38 (2022), no. 1, pp. 95–111DOI 10.4171/RMI/1272