Geodesic
Sufficient conditions for local quasiconformality of mappings with bounded distortion
Sbornik. Mathematics, Tome 78 (1994) no. 2, pp. 437-445 
I. V. Zhuravlev. Sufficient conditions for local quasiconformality of mappings with bounded distortion. Sbornik. Mathematics, Tome 78 (1994) no. 2, pp. 437-445. http://geodesic.mathdoc.fr/item/SM_1994_78_2_a10/
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     title = {Sufficient conditions for local quasiconformality of mappings with bounded distortion},
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Voir la notice de l'article provenant de la source Math-Net.Ru

Sufficient conditions for a mapping $f(x)$ with bounded distortion to be a local homeomorphism are established in terms of estimates of the oscillation of its normalized Jacobi matrix $$ f'(x)/\lvert\det f'(x)\rvert^{1/n}. $$ The results obtained are used in the description of properties of the solutions of the system of partial differential equations $$ f'(x)=K(x)\lvert\det f'(x)\rvert^{1/n}, $$ where $K(x)$ is a given matrix-valued function.

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