Smooth approximation of bi-Lipschitz orientation-preserving homeomorphisms

Daneri, Sara; Pratelli, Aldo

Annales de l'I.H.P. Analyse non linéaire, Tome 31 (2014) no. 3, pp. 567-589.

We show that a planar bi-Lipschitz orientation-preserving homeomorphism can be approximated in the $W^{1,p}$ norm, together with its inverse, with an orientation-preserving homeomorphism which is piecewise affine or smooth.

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