Structure of level sets and Sard-type properties of Lipschitz maps

Alberti, Giovanni; Bianchini, Stefano; Crippa, Gianluca

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 12 (2013) no. 4, pp. 863-902.

We consider certain properties of maps of class $C^2$ from ${ℝ}^d$ to ${ℝ}^{d-1}$ that are strictly related to Sard’s theorem, and we show that some of them can be extended to Lipschitz maps, while others require some additional regularity. We also give examples showing that, in terms of regularity, our results are optimal.

Classification : 26B35, 26B10, 26B05, 49Q15, 58C25

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