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 **R**^{n}, *n* \ge 2, and
let *f* be a continuous mapping of \overline *D* into
**R**^{n} 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(2*t*) \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

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