Calculus of Variations and Geometric Measure Theory
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G. Alberti - S. Bianchini - G. Crippa

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

created by crippa on 24 Jul 2011
modified by alberti on 12 Feb 2014


Published Paper

Inserted: 24 jul 2011
Last Updated: 12 feb 2014

Journal: Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5)
Volume: 12
Number: 4
Pages: 863-902
Year: 2013
Doi: 10.2422/2036-2145.201107_006


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 show that some of them can be extended to Lipschitz maps, while others still require some additional regularity. We also give counterexamples showing that, in term of regularity, our results are optimal.

Keywords: weak Sard property, lipschitz maps, level sets, critical set, Sard's theorem, distributional divergence


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