Abstract
We prove the following theorem: every quasiconformal harmonic mapping between two plane domains with C1,α (α < 1) and, respectively, C1,1 compact boundary is bi-Lipschitz. This theorem extends a similar result of the author [10] for Jordan domains, where stronger boundary conditions for the image domain were needed. The proof uses distance function from the boundary of the image domain. Mathematics Subject Classification (2010): 58E20 (primary); 30C62 (secondary).
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