A simple proof of the Morse-Sard theorem in Sobolev spaces
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- Proc. Amer. Math. Soc. 136 (2008), 3675-3681 Request permission
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.References
- Ralph Abraham and Joel Robbin, Transversal mappings and flows, W. A. Benjamin, Inc., New York-Amsterdam, 1967. An appendix by Al Kelley. MR 0240836
- S. M. Bates, Toward a precise smoothness hypothesis in Sard’s theorem, Proc. Amer. Math. Soc. 117 (1993), no. 1, 279–283. MR 1112486, DOI 10.1090/S0002-9939-1993-1112486-4
- Luigi de Pascale, The Morse-Sard theorem in Sobolev spaces, Indiana Univ. Math. J. 50 (2001), no. 3, 1371–1386. MR 1871360, DOI 10.1512/iumj.2001.50.1878
- Lawrence C. Evans and Ronald F. Gariepy, Measure theory and fine properties of functions, Studies in Advanced Mathematics, CRC Press, Boca Raton, FL, 1992. MR 1158660
- Jan Malý, David Swanson, and William P. Ziemer, The co-area formula for Sobolev mappings, Trans. Amer. Math. Soc. 355 (2003), no. 2, 477–492. MR 1932709, DOI 10.1090/S0002-9947-02-03091-X
Additional Information
- 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
- 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
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 2415054