We prove a version of the Inverse Function Theorem for continuous weakly differentiable mappings. Namely, a nonconstant mapping is a local homeomorphism if it has integrable inner distortion function and satisfies a certain differential inclusion. The integrability assumption is shown to be optimal.
Keywords: Local homeomorphism, Differential inclusion, Finite distortion
@article{AIHPC_2010__27_2_517_0, author = {Kovalev, Leonid V. and Onninen, Jani and Rajala, Kai}, title = {Invertibility of {Sobolev} mappings under minimal hypotheses}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {517--528}, publisher = {Elsevier}, volume = {27}, number = {2}, year = {2010}, doi = {10.1016/j.anihpc.2009.09.010}, mrnumber = {2595190}, zbl = {1190.30019}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.anihpc.2009.09.010/} }
TY - JOUR AU - Kovalev, Leonid V. AU - Onninen, Jani AU - Rajala, Kai TI - Invertibility of Sobolev mappings under minimal hypotheses JO - Annales de l'I.H.P. Analyse non linéaire PY - 2010 SP - 517 EP - 528 VL - 27 IS - 2 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.anihpc.2009.09.010/ DO - 10.1016/j.anihpc.2009.09.010 LA - en ID - AIHPC_2010__27_2_517_0 ER -
%0 Journal Article %A Kovalev, Leonid V. %A Onninen, Jani %A Rajala, Kai %T Invertibility of Sobolev mappings under minimal hypotheses %J Annales de l'I.H.P. Analyse non linéaire %D 2010 %P 517-528 %V 27 %N 2 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.anihpc.2009.09.010/ %R 10.1016/j.anihpc.2009.09.010 %G en %F AIHPC_2010__27_2_517_0
Kovalev, Leonid V.; Onninen, Jani; Rajala, Kai. Invertibility of Sobolev mappings under minimal hypotheses. Annales de l'I.H.P. Analyse non linéaire, Volume 27 (2010) no. 2, pp. 517-528. doi : 10.1016/j.anihpc.2009.09.010. http://archive.numdam.org/articles/10.1016/j.anihpc.2009.09.010/
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