Estimates for the dilatation of -harmonic mappings
Alessandrini, G. - Nesi, V.

Abstract. We consider planar σ-harmonic mappings, that is mappings U whose components up1 and u² solve a divergence structure elliptic equation div(σ∇uⁱ)=0, for i = 1, 2.
We investigate whether a locally invertible σ-harmonic mapping U is also quasiconformal. Under mild regularity assumptions, only involving det σ and the antisymmetric part of σ, we prove quantitative bounds which imply quasiconformality

Rend. Mat. Appl. (7) 35 (2014) 215-225; pdf