Sobolev spaces revisited
Sobolev spaces revisited
We describe a recent, one-parameter family of characterizations of Sobolev and BV functions on \mathbb{R}^n n, using sizes of superlevel sets of suitable difference quotients. This provides an alternative point of view to the BBM formula by Bourgain, Brezis, and Mironescu, and complements in the case of BV some results …