Generalized N-property and Sard theorem for Sobolev maps

Abstract

I report on some recent extensions of the Lusin N-property and the Sard theorem for Sobolev maps, which have been obtained in a joint work with M. Csörnyei, E. D’Aniello, and B. Kirchheim. Our research was originally motivated by questions related to the uniqueness of weak solutions for the continuity equation associated to a vector field with Sobolev regularity.