Mappings by solutions of strongly elliptic systems

Boundary properties and univalence of solutions of strongly elliptic systems of 2-nd order on the plane are discussed. The most studied are the mappings by complex-valued harmonic functions. Such mappings can often be "lifted" to mappings of surfaces. We give an example of a mapping by the Poisson kernel for a plane Lame system, which can also be naturally associated with a mapping of surfaces, but, in contrast to the harmonic case, the method of "lifting" a mapping in a more general situation is still unclear.