On the Morse-Sard Property and Level Sets of Sobolev and BV Functions
By Jean Bourgain, M. Korobkov, Jan Kristensen. 2010
68 citations recorded by the source corpus.
We establish Luzin $N$ and Morse-Sard properties for $BV_2$-functions defined on open domains in the plane. Using these results we prove that almost all level sets are finite disjoint unions of Lipschitz arcs whose tangent vectors are of bounded variation. In the case of $W^{2,1}$-functions we strengthen the conclusion and show that almost all level sets are finite disjoint unions of $C^1$-arcs whose tangent vectors are absolutely continuous.
Subfields: Applied Mathematics
View Paper: https://www.semanticscholar.org/paper/7977cdfd40a24bd30e14407ffa1ab4cbe9a32d31
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In Applied Mathematics
- Gianluca Crippa
- Giovanni S. Alberti
- Stefano Bianchini
- Luigi Ambrosio
- Xicheng Zhang
- Dario Trevisan
- Pierre-Emmanuel Jabin
- Sylvia Serfaty
Citations in the corpus
- Structure of level sets and Sard-type properties of Lipschitz maps (2013, background): “Through the rest of this paper, sets and functions are tacitly assumed to be Borel measurable, and measures are always defined on the appropriate Borel σ-algebra.”