Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 37, 2012, 107-118

BOUNDARY MODULUS OF CONTINUITY AND QUASICONFORMAL MAPPINGS

Milos Arsenovic, Vesna Manojlovic and Raimo Näkki

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

University of Belgrade, Faculty of Organizational Sciences
Jove Ilica 154, 11000 Belgrade, Serbia; vesnam 'at' fon.bg.ac.rs

University of Jyväskylä, Department of Mathematics and Statistics
P.O. Box 35 (MaD), FI-40014 Jyväskylä, Finland; raimon 'at' maths.jyu.fi

Abstract. Let D be a bounded domain in Rⁿ, n \ge 2, and let f be a continuous mapping of \overline D into Rⁿ which is quasiconformal in D. Suppose that |f(x) - f(y)| \le \omega(|x - y|) for all x and y in \partial D, where \omega is a non-negative non-decreasing function satisfying \omega(2t) \le 2\omega(t) for t \ge 0. We prove, with an additional growth condition on \omega, that |f(x) - f(y)| \le C max{\omega(|x - y|), |x - y|^\alpha} for all x,y \in D, where \alpha = K_I(f)^1/(1-n).

2010 Mathematics Subject Classification: Primary 30C65.

Key words: Quasiconformal mapping, modulus of continuity.

Reference to this article: M. Arsenovic, V. Manojlovic and R. Näkki: Boundary modulus of continuity and quasiconformal mappings. Ann. Acad. Sci. Fenn. Math. 37 (2012), 107-118.

Full document as PDF file

doi:10.5186/aasfm.2012.3718