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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
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  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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