On the Morse-Sard Theorem for the sharp case of Sobolev mappings Mikhail KorobkovJan Kristensen 58K0546E35Sobolev-Lorentz spaceLuzin N propertyMorse-Sardlevel sets 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 $n-m$. Indiana University Mathematics Journal 2014 text pdf 10.1512/iumj.2014.63.5431 10.1512/iumj.2014.63.5431 en Indiana Univ. Math. J. 63 (2014) 1703 - 1724 state-of-the-art mathematics http://iumj.org/access/