We consider certain properties of maps of class C 2 from Rd to Rd−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.
A uniqueness result for the continuity equation in two dimensions / Alberti, G.; Bianchini, Stefano; Crippa, G.. - In: JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY. - ISSN 1435-9855. - 16:2(2014), pp. 201-234. [10.4171/JEMS/431]
A uniqueness result for the continuity equation in two dimensions
Bianchini, Stefano;
2014-01-01
Abstract
We consider certain properties of maps of class C 2 from Rd to Rd−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.File in questo prodotto:
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