Variationscharakterisierungen für gewisse quasikonforme Abbildungen

Abstract

The paper deals with the construction of solutions $f$ for the equation $f_{\bar{z}}(z)=v(z)\overline{f_z(z)}$ with $v(z)=0$ in a neighbourhood of $\infty$. In the paper two variational methods are described. The first method characterizes $f$ for a bounded and measurable function $v(0\le v(z)\le q=\mathrm{const}<1$. If $v$ is a piecewise constant function, then there exists also a simpler characterization of $f$.