article

Title: On the Morse-Sard Theorem for the sharp case of Sobolev mappings

Authors: Mikhail Korobkov and Jan Kristensen

Issue: Volume 63 (2014), Issue 6, 1703-1724

Abstract:

$We establish Luzin $N$- and Morse-Sard properties for mappings $v\colon\mathbb{R}^n\to\mathbb{R}^m$ of the Sobolev-Lorentz class $\mathrm{W}^k_{p,1}$ with $k=n-m+1$ and $p=n/k$ (this is the sharp case that guaranties the continuity of mappings). Using these results, we prove that almost all level sets are finite disjoint unions of $\mathrm{C}^1$-smooth compact manifolds of dimension $n-m$.$