JournalsaihpcVol. 27, No. 2pp. 517–528

Invertibility of Sobolev mappings under minimal hypotheses

  • Kai Rajala

    Department of Mathematics and Statistics, University of Jyväskylä, PO Box 35 (MaD), FI-40014, University of Jyväskylä, Finland

  • Leonid V. Kovalev

    Department of Mathematics, Syracuse University, Syracuse, NY 13244, USA

  • Jani Onninen

    Department of Mathematics, Syracuse University, Syracuse, NY 13244, USA
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Abstract

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.

Cite this article

Kai Rajala, Leonid V. Kovalev, Jani Onninen, Invertibility of Sobolev mappings under minimal hypotheses. Ann. Inst. H. Poincaré Anal. Non Linéaire 27 (2010), no. 2, pp. 517–528

DOI 10.1016/J.ANIHPC.2009.09.010