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Proceedings of the American Mathematical Society

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A simple proof of the Morse-Sard theorem in Sobolev spaces


Author: Alessio Figalli
Journal: Proc. Amer. Math. Soc. 136 (2008), 3675-3681
MSC (2000): Primary 58C25; Secondary 46T20
DOI: https://doi.org/10.1090/S0002-9939-08-09321-0
Published electronically: May 23, 2008
MathSciNet review: 2415054
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Abstract: In this paper we give a new simple proof of a result of Luigi De Pascale, which states that the Morse-Sard Theorem holds under the hypothesis of Sobolev regularity. Moreover, as our proof is independent of the Morse-Sard Theorem with $ C^k$ regularity, our result implies the classical Morse-Sard Theorem.


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Alessio Figalli
Affiliation: Université de Nice Sophia-Antipolis, Laboratoire J.-A. Dieudonné, CNRS UMR 6621, Parc Valrose, 06108 Nice Cedex 02, France
Email: figalli@unice.fr

DOI: https://doi.org/10.1090/S0002-9939-08-09321-0
Keywords: Sard theorem, Sobolev spaces
Received by editor(s): April 6, 2006
Received by editor(s) in revised form: June 20, 2006
Published electronically: May 23, 2008
Communicated by: David Preiss
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.