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arXiv · 1810.03003

Locally invertible $\sigma$-harmonic mappings

Giovanni Alessandrini·Vincenzo Nesi
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Abstract

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.

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Giovanni Alessandrini, Vincenzo Nesi. 2018-10-06. Locally invertible $\sigma$-harmonic mappings. https://arxiv.org/abs/1810.03003

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