Mathematics – Complex Variables
Scientific paper
2010-11-12
Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5), Vol. X (2011), 669-681
Mathematics
Complex Variables
10 pages, to appear in Annali della Scuola Normale Superiore di Pisa, Classe di Scienze
Scientific paper
We prove the following theorem: every quasiconformal harmonic mapping between two plane domains with $C^{1,\alpha}$ ($\alpha<1$), respectively $C^{1,1}$ compact boundary is bi-Lipschitz. The distance function with respect to the boundary of the image domain is used. This in turn extends a similar result of the author in \cite{kalajan} for Jordan domains, where stronger boundary conditions for the image domain were needed.
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