Estimates for the dilatation of $\sigma$-harmonic mappings
Giovanni Alessandrini, Vincenzo Nesi · arXiv (Cornell University) · 2014
We consider planar $\\sigma$-harmonic mappings, that is mappings $U$ whose components $u^1$ and $u^2$ solve a divergence structure elliptic equation ${\\rm div} (\\sigma \ abla u^i)=0$, for $i=1,2$. We investigate whether a locally invertible $ \\sigma$-harmonic mapping $U$ is also quasiconformal. Under mild regularity assumptions, only involving $\\det \\sigma$ and the antisymmetric part of $\\sigma$, we prove quantitative bounds which imply quasiconformality.