Harmonic mappings and distance function
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 10 (2011) no. 3, p. 669-681

We prove the following theorem: every quasiconformal harmonic mapping between two plane domains with C 1,α (α<1) and, respectively, C 1,1 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.

Published online : 2018-06-21
Classification:  58E20,  30C62
@article{ASNSP_2011_5_10_3_669_0,
     author = {Kalaj, David},
     title = {Harmonic mappings and distance function},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 10},
     number = {3},
     year = {2011},
     pages = {669-681},
     zbl = {1252.30018},
     mrnumber = {2905382},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_2011_5_10_3_669_0}
}
Kalaj, David. Harmonic mappings and distance function. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 10 (2011) no. 3, pp. 669-681. http://www.numdam.org/item/ASNSP_2011_5_10_3_669_0/

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