We extend the Rado-Choquet-Kneser theorem to mappings with Lipschitz boundary data and essentially positive Jacobian at the boundary without restriction on the convexity of image domain. The proof is based on a recent extension of the Rado-Choquet-Kneser theorem by Alessandrini and Nesi and it uses an approximation scheme. Some applications to families of quasiconformal harmonic mappings between Jordan domains are given.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm207-2-2,
author = {David Kalaj},
title = {Invertible harmonic mappings beyond the Kneser theorem and quasiconformal harmonic mappings},
journal = {Studia Mathematica},
volume = {204},
year = {2011},
pages = {117-136},
zbl = {1279.30032},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm207-2-2}
}
David Kalaj. Invertible harmonic mappings beyond the Kneser theorem and quasiconformal harmonic mappings. Studia Mathematica, Tome 204 (2011) pp. 117-136. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm207-2-2/