On the Morse–Sard property and level sets of Sobolev and BV functions Full article
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Revista Matematica Iberoamericana
ISSN: 0213-2230 |
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| Output data | Year: 2013, Volume: 29, Number: 1, Pages: 1-23 Pages count : 23 DOI: 10.4171/rmi/710 | ||||||||
| Tags | BV2 and W2,1 functions; Level sets; Luzin N property; Morse-Sard property | ||||||||
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Abstract:
We establish Luzin N and Morse–Sard properties for BV2 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 W2,1 functions we strengthen the conclusion and show that almost all level sets are finite disjoint unions of C1 arcs whose tangent vectors are absolutely continuous along these arcs.
Cite:
Bourgain J.
, Korobkov M.
, Kristensen J.
On the Morse–Sard property and level sets of Sobolev and BV functions
Revista Matematica Iberoamericana. 2013. V.29. N1. P.1-23. DOI: 10.4171/rmi/710 WOS Scopus OpenAlex
On the Morse–Sard property and level sets of Sobolev and BV functions
Revista Matematica Iberoamericana. 2013. V.29. N1. P.1-23. DOI: 10.4171/rmi/710 WOS Scopus OpenAlex
Identifiers:
| Web of science: | WOS:000317157600001 |
| Scopus: | 2-s2.0-84876789647 |
| OpenAlex: | W2963645786 |