Invertibility of Sobolev mappings under minimal hypotheses
Annales de l'I.H.P. Analyse non linéaire, Volume 27 (2010) no. 2, p. 517-528

We prove a version of the Inverse Function Theorem for continuous weakly differentiable mappings. Namely, a nonconstant W 1,n 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.

DOI : https://doi.org/10.1016/j.anihpc.2009.09.010
Classification:  30C65,  26B10,  26B25
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},
     publisher = {Elsevier},
     volume = {27},
     number = {2},
     year = {2010},
     pages = {517-528},
     doi = {10.1016/j.anihpc.2009.09.010},
     zbl = {1190.30019},
     mrnumber = {2595190},
     language = {en},
     url = {http://www.numdam.org/item/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://www.numdam.org/item/AIHPC_2010__27_2_517_0/

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