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

2008
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Proceedings of the American Mathematical Society
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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. The Morse-Sard Theorem is concerned with the size of the image of the critical values of a differentiable function. To recall it and to state our result, we need some definitions. Definition 1 Let

doi:10.1090/s0002-9939-08-09321-0
fatcat:m7qgqivcxneq7jqzu5ssvbl5r4