Author:
Grigoryan Armen,Michalski Andrzej,Partyka Dariusz
Abstract
AbstractLet I be a line segment in the complex plane $$\mathbb C$$
C
. We describe a method of constructing a bi-Lipschitz sense-preserving mapping of $$\mathbb C$$
C
onto itself, which is harmonic in $$\mathbb C\setminus I$$
C
\
I
and coincides with a given sufficiently regular function $$f:I\rightarrow \mathbb C$$
f
:
I
→
C
. As a result we show that a quasiconformal self-mapping of $$\mathbb C$$
C
which is harmonic in $$\mathbb C\setminus I$$
C
\
I
does not have to be harmonic in $$\mathbb C$$
C
.
Publisher
Springer Science and Business Media LLC
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