On the Morse–Sard property and level sets of Wn,1 Sobolev functions on ℝn

On the Morse–Sard property and level sets of Wn,1 Sobolev functions on ℝn Full article

Journal

Journal fur die Reine und Angewandte Mathematik
ISSN: 0075-4102 , E-ISSN: 1435-5345

Output data

Year: 2013, Volume: 2015, Number: 700, Pages: 93-112 Pages count : 20 DOI: 10.1515/crelle-2013-0002

Authors

Bourgain Jean ¹ , Korobkov Mikhail V. ² , Kristensen Jan ³

Affiliations

1	School of Mathematics, Institute for Advanced Study, Einstein Drive
2	Sobolev Institute of Mathematics
3	Mathematical Institute, University of Oxford

Abstract. We establish Luzin N- and Morse-Sard properties for functions from the Sobolev space W^{n,1}(R^n) Using these results we prove that almost all level sets are finite disjoint unions of C1-smooth compact manifolds of dimension n-1. These results remain valid also within the larger space of functions of bounded variation BVn.Rn/. For the proofs we establish and use some new results on Luzin-type approximation of Sobolev and BV-functions by Ck-functions, where the exceptional sets have small Hausdorff content.

Bourgain J. , Korobkov M.V. , Kristensen J.
On the Morse–Sard property and level sets of Wn,1 Sobolev functions on ℝn
Journal fur die Reine und Angewandte Mathematik. 2013. V.2015. N700. P.93-112. DOI: 10.1515/crelle-2013-0002 WOS Scopus OpenAlex

Web of science:	WOS:000350640900003
Scopus:	2-s2.0-84925680110
OpenAlex:	W2334279071

DB	Citing
Scopus	22
OpenAlex	32
Web of science	20