Annales Academię Scientiarum Fennicę
Mathematica
Volumen 34, 2009, 475-485

LIPSCHITZ SPACES AND HARMONIC MAPPINGS

David Kalaj

University of Montenegro, Faculty of Natural Sciences and Mathematics
Cetinjski put b.b. 81000 Podgorica, Montenegro; davidk 'at' cg.yu

Abstract. In [11] the author proved that every quasiconformal harmonic mapping between two Jordan domains with C^1,\alpha, 0 < \alpha \le 1, boundary is bi-Lipschitz, providing that the domain is convex. In this paper we avoid the restriction of convexity. More precisely we prove: any quasiconformal harmonic mapping between two Jordan domains \Omega_j, j = 1,2, with C^j,\alpha, j = 1,2 boundary is bi-Lipschitz.

2000 Mathematics Subject Classification: Primary 30C55; Secondary 31C62.

Key words: Quasiconformal harmonic maps, Jordan domains, Lipschitz condition.

Reference to this article: D. Kalaj: Lipschitz spaces and harmonic mappings. Ann. Acad. Sci. Fenn. Math. 34 (2009), 475-485.

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