Annales Academić Scientiarum Fennicć
Mathematica
Volumen 38, 2013, 839-847

MODULI OF CONTINUITY OF HARMONIC QUASIREGULAR MAPPINGS ON BOUNDED DOMAINS

Ali Abaob, Milos Arsenovic, Miodrag Mateljevic and Abejela Shkheam

University of Belgrade, Faculty of Mathematics
Studentski Trg 16, 11000 Belgrade, Serbia; elhrarya 'at' yahoo.com

University of Belgrade, Faculty of Mathematics
Studentski Trg 16, 11000 Belgrade, Serbia; arsenovic 'at' matf.bg.ac.rs

University of Belgrade, Faculty of Mathematics
Studentski Trg 16, 11000 Belgrade, Serbia; miodrag 'at' matf.bg.ac.rs

University of Belgrade, Faculty of Mathematics
Studentski Trg 16, 11000 Belgrade, Serbia; abejelashkhea 'at' yahoo.com

Abstract. We prove that \omega_u(\delta) \leq C\omega_f(\delta), where u : \overline{\Omega} -> Rⁿ is the harmonic extension of a continuous map f -> \partial{\Omega} -> Rⁿ, if u is a K-quasiregular map and \Omega is bounded in Rⁿ with C2 boundary. Here C is a constant depending only on n, \omega_f and K and \omega_h denotes the modulus of continuity of h. We also prove a version of this result for \Lambda_\omega-extension domains with c-uniformly perfect boundary and quasiconformal mappings.

2010 Mathematics Subject Classification: Primary 30C80, 30C62; Secondary 30C55, 30H05.

Key words: Lipschitz-type spaces, harmonic mappings, quasiregular mappings, uniform domains.

Reference to this article: A. Abaob, M. Arsenovic, M. Mateljevic and A. Shkheam: Moduli of continuity of harmonic quasiregular mappings on bounded domains. Ann. Acad. Sci. Fenn. Math. 38 (2013), 839-847.

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doi:10.5186/aasfm.2013.3848