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

Author(s): Alessio Figalli
Journal: Proc. Amer. Math. Soc. 136 (2008), 3675-3681.
MSC (2000): Primary 58C25; Secondary 46T20
Posted: May 23, 2008
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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 regularity, our result implies the classical Morse-Sard Theorem.

References:

1.: R. ABRAHAM AND J. ROBBIN: Transversal Mappings and Flows. W. A. Benjamin, Inc., New York-Amsterdam, 1967. MR 0240836 (39:2181)
2.: S.M. BATES: Toward a precise smoothness hypothesis in Sard's theorem. Proc. Amer. Math. Soc., 117 (1993), no. 1, 279-283. MR 1112486 (93c:58028)
3.: L. DE PASCALE: The Morse-Sard theorem in Sobolev spaces. Indiana Univ. Math. J., 50 (2001), no. 3, 1371-1386. MR 1871360 (2002k:58018)
4.: L.C. EVANS AND R.F. GARIEPY: Measure Theory and Fine Properties of Functions. Studies in Advanced Mathematics, CRC Press, Boca Raton, FL, 1992. MR 1158660 (93f:28001)
5.: J. MALY, D. SWANSON AND W.P. ZIEMER: The co-area formula for Sobolev mappings. Trans. Amer. Math. Soc., 355 (2003), no. 2, 477-492. MR 1932709 (2004a:46037)

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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

DOI: 10.1090/S0002-9939-08-09321-0
PII: S 0002-9939(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
Posted: May 23, 2008
Communicated by: David Preiss
Copyright of article: Copyright 2008, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.


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