Invertibility of Sobolev mappings under minimal hypotheses |
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| Authors: | Leonid V. Kovalev Jani Onninen Kai Rajala |
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| Affiliation: | 1. Department of Mathematics, Syracuse University, Syracuse, NY 13244, USA;2. Department of Mathematics and Statistics, University of Jyväskylä, PO Box 35 (MaD), FI-40014, University of Jyväskylä, Finland |
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| Abstract: | We prove a version of the Inverse Function Theorem for continuous weakly differentiable mappings. Namely, a nonconstant W1,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. |
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| Keywords: | primary, 30C65 secondary, 26B10, 26B25 |
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