Invertibility of Sobolev mappings under minimal hypotheses

Kovalev, Leonid V.; Onninen, Jani; Rajala, Kai

doi:10.1016/j.anihpc.2009.09.010

Kovalev, Leonid V. ; Onninen, Jani ; Rajala, Kai

Annales de l'I.H.P. Analyse non linéaire, Tome 27 (2010) no. 2, pp. 517-528.

Résumé

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.

MR Zbl

DOI : 10.1016/j.anihpc.2009.09.010

Classification : 30C65, 26B10, 26B25
Mots-clés : Local homeomorphism, Differential inclusion, Finite distortion

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     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},
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     zbl = {1190.30019},
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     url = {http://www.numdam.org/articles/10.1016/j.anihpc.2009.09.010/}
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Kovalev, Leonid V.; Onninen, Jani; Rajala, Kai. Invertibility of Sobolev mappings under minimal hypotheses. Annales de l'I.H.P. Analyse non linéaire, Tome 27 (2010) no. 2, pp. 517-528. doi : 10.1016/j.anihpc.2009.09.010. http://www.numdam.org/articles/10.1016/j.anihpc.2009.09.010/

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