We show that a planar bi-Lipschitz orientation-preserving homeomorphism can be approximated in the norm, together with its inverse, with an orientation-preserving homeomorphism which is piecewise affine or smooth.
@article{AIHPC_2014__31_3_567_0, author = {Daneri, Sara and Pratelli, Aldo}, title = {Smooth approximation of bi-Lipschitz orientation-preserving homeomorphisms}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, volume = {31}, year = {2014}, pages = {567-589}, doi = {10.1016/j.anihpc.2013.04.007}, mrnumber = {3208455}, zbl = {1348.37071}, language = {en}, url = {http://dml.mathdoc.fr/item/AIHPC_2014__31_3_567_0} }
Daneri, Sara; Pratelli, Aldo. Smooth approximation of bi-Lipschitz orientation-preserving homeomorphisms. Annales de l'I.H.P. Analyse non linéaire, Tome 31 (2014) pp. 567-589. doi : 10.1016/j.anihpc.2013.04.007. http://gdmltest.u-ga.fr/item/AIHPC_2014__31_3_567_0/
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