Families of functionals representing Sobolev norms

Haim Brezis, Andreas Seeger, Jean Van Schaftingen +1

We obtain new characterizations of the Sobolev spaces ${\dot{W}}^{1,p}({\mathbb{R}}^N)$ and the bounded variation space $\dot{BV}({\mathbb{R}}^N)$. The characterizations are in terms of t…