Locally invertible σ--harmonic mappings.
Giovanni Alessandrini, Vincenzo Nesi

Abstract. We extend a classical theorem by H. Lewy to planar σ-harmonic mappings, that is mappings U whose components u¹ and u² solve a divergence structure elliptic equation div (σ∇ uⁱ)=0, for i=1,2. A similar result is established for pairs of solutions of certain second order non--divergence equations.

Rend. Mat. Appl. (7) 39 (2018) 195-203; pdf