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

Journal article

We establish Luzin N and Morse–Sard properties for functions from the Sobolev space Wn,1(Rn). 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.

Authors: Bourgain, J; Korobkov, M; Kristensen, J

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: De Gruyter
• Journal: Journal für die reine und angewandte Mathematik
• Volume: 2015
• Issue: 700
• Pages: 93–112
• Publication date: 2013-03-16
• DOI: 10.1515/crelle-2013-0002
• EISSN: 1435-5345
• ISSN: 0075-4102
• Language: English