On p-harmonic mappings in the plane Original Research Article

To every pp-harmonic vector field in the plane with p≥2p≥2 there corresponds a quasilinear system of first order PDEs which couples the complex gradients of the coordinate functions of the field. The ellipticity of such system is proved. A relation between planar quasiregular mappings and pp-harmonic fields is discussed. The pp-harmonic conjugate problem is stated.