We consider certain properties of maps of class C-2 from R-d to Rd-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.
Structure of level sets and Sard-type properties of Lipschitz maps / Alberti, G.; Bianchini, S.; Crippa, G.. - In: ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA. CLASSE DI SCIENZE. - ISSN 0391-173X. - 12:4(2013), pp. 863-902. [10.2422/2036-2145.201107_006]
Structure of level sets and Sard-type properties of Lipschitz maps
Bianchini, S.;
2013-01-01
Abstract
We consider certain properties of maps of class C-2 from R-d to Rd-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.File in questo prodotto:
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