A simple proof of the Morse-Sard theorem in Sobolev spaces
By Alessio Figalli. 2008
53 citations recorded by the source corpus.
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.
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/ab540d47c679154dafcab7aafde98d594822a41b
How researchers see this paper
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In Applied Mathematics
- Jan Kristensen
- Elia Brué
- M. Korobkov
- Daniele Semola
- Jean Bourgain
- Giuseppe Mingione
- Jean Van Schaftingen
- Larry Guth
In Mathematical Physics
- Elia Brué
- M. Korobkov
- Daniele Semola
- Jan Kristensen
- Jean Bourgain
- P. P. Varj'u
- Larry Guth
- Massimiliano Berti
Citations in the corpus
- Constancy of the Dimension for RCD(K,N) Spaces via Regularity of Lagrangian Flows (2018, background): “ 3.1 above resembles the part of the proof of Sard’s lemma where it is shown that the image of the set of points where all the derivatives vanish up to a certain order is negligible (see for instance [F08]). Recall that the classical Sard’s lemma requires some regularity of the map and that the high”
- Structure of level sets and Sard-type properties of Lipschitz maps (2013, unknown): “2 For Sard’s Theorem for maps of class C(1,1) see [2], for maps in the Sobolev class W 2,p see [4, 5, 10].”
- On the Morse-Sard Property and Level Sets of Sobolev and BV Functions (2010, methodology): “In particular, we mention the work [12] of De Pascale (see also [17])”