Members’ Seminar

This talk is motivated by some recent work of Bourgain- rezis-Mironescu. A few years ago, they introduced an elementary way of defining the Sobolev spaces $W^{1,p}$ without making any use of derivatives. I will present their definition and some applications. I will conclude with some new estimates they have proved for the topological degree of maps $g : S^N \to S^N$.