Mathematics

 In 1934 H. Whitney posed the following Problem: How can one tell whether a given function $f$ defined on arbitrary subset $S \subset \mathbb{R}^{n}$ extends to a $C^{m}(\mathbb{R}^{n})$ function? Surprisingly, this problem was solved only recently by C. Fefferman. Starting from that paper generalization of the classical Whitney Problem in the context of Sobolev Spaces is of great interest. We are going to describe recent progress in this area.