\(\mu(z)\)-homeomorphisms in the plane
This paper deals with \(\mu(z)\) homeomorphisms of a domain \(\Omega\) of the complex plane, that are topological mappings which are \(ACL\) in \(\Omega\) and satisfy the Beltrami equation \[ f_{\overline{z}}(z) = \mu(z) f_z(z), \;z \in \Omega, \] where \(\mu(z)\) is a measurable function with \(| \mu(z)| <1\). Let \(D(z)= \frac{1+| \mu(z)| }{1-| \mu(z)| }\) the dilatation function, then an existence and a uniqueness theorem is proven under the assumptions that \(D(z)\) is locally in \(L^\lambda (C)\) for some \(\lambda > 1\) and under conditions for the integral mean of \(D(z)\).
scientific article; zbMATH DE number 2075170