Locally invertible $\sigma$-harmonic mappings
Locally invertible $\sigma$-harmonic mappings
We extend a classical theorem by H. Lewy to planar $\sigma$-harmonic mappings, that is mappings $U$ whose components $u^1$ and $u^2$ solve a divergence structure elliptic equation ${\rm div} (\sigma \nabla u^i)=0$ , for $i=1,2$. A similar result is established for pairs of solutions of certain second order non--divergence equations.
Comment: 8 pages
- University of Trieste Italy
elliptic equations, Elliptic equation, Quasiconformal mappings in the complex plane, Beltrami operator, Mathematics - Analysis of PDEs, Second-order elliptic systems, quasiconformal mappings, 30C62, 35J55, Beltrami operators, Elliptic equations; Beltrami operators; quasiconformal mappings
elliptic equations, Elliptic equation, Quasiconformal mappings in the complex plane, Beltrami operator, Mathematics - Analysis of PDEs, Second-order elliptic systems, quasiconformal mappings, 30C62, 35J55, Beltrami operators, Elliptic equations; Beltrami operators; quasiconformal mappings
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