The first part of talk is based on joint papers [1]-[3]. We establish Luzin N- and Morse-Sard properties for mappings f : Rn→Rm of the Sobolev-Lorentz class Wkp,1 with k = n - m + 1 and p = n/k (this is the sharp case that guaranties the continuity of mappings; for values k = n, p = 1 the Sobolev-Lorentz class Wn1,1(Rn) coincides with the usual Sobolev space Wn1 (Rn)). Using these results we prove that almost all level sets of f are finite disjoint unions of C1-smooth compact manifolds of dimension n - m (despite the fact that f itself is not C1 ) .

海报