Joint BCAM-UPV/EHU Analysis and PDE seminar: Limiting embedding of Fractional Sobolev Spaces

The  Bourgain-Brezis-Mironescu(BBM) formula gives us a way to express the Sobolev seminorms in terms of the fractional Sobolev seminorms and thus gives an alternative characterization of Sobolev spaces without the notion of weak derivatives.  In this talk, I shall discuss the origin and some recent developments on the extensions of the BBM formula. In the first part of the talk, I shall discuss the case of Sobolev extension domains, and in the second part, I shall talk about BBM formula for spaces related to Triebel-Lizorkin spaces.

Part of the results in this talk are based on a joint work with Kaushik Bal and Prosenjit Roy.