Annales Academię Scientiarum Fennicę
Mathematica
Volumen 33, 2008, 315-318

ON LIPSCHITZ CONTINUITY OF HARMONIC QUASIREGULAR MAPS ON THE UNIT BALL IN Rⁿ

Milos Arsenovic, Vesna Kojic and Miodrag Mateljevic

University of Belgrade, Faculty of Mathematics
Studentski Trg 16, Belgrade, Serbia; arsenovic 'at' matf.bg.ac.yu

University of Belgrade, Faculty of Organizational Sciences
Jove Ilica 154, Belgrade, Serbia; vesnak 'at' fon.bg.ac.yu

University of Belgrade, Faculty of Mathematics
Studentski Trg 16, Belgrade, Serbia; miodrag 'at' matf.bg.ac.yu

Abstract. We show that Lipschitz continuity of \phi : S^n-1 -> Rⁿ implies Lipschitz continuity of its harmonic extension u = P[\phi] : Bⁿ -> Rⁿ, provided u is a quasiregular map.

2000 Mathematics Subject Classification: Primary 31B25; Secondary 30C65, 31B05.

Key words: Quasiregular mappings, harmonic mappings, Lipschitz spaces.

Reference to this article: M. Arsenovic, V. Kojic and M. Mateljevic: On Lipschitz continuity of harmonic quasiregular maps on the unit ball in Rⁿ. Ann. Acad. Sci. Fenn. Math. 33 (2008), 315-318.

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