A remake of Bourgain–Brezis–Mironescu characterization of Sobolev spaces
A remake of Bourgain–Brezis–Mironescu characterization of Sobolev spaces
Abstract We introduce a large class of concentrated p -Lévy integrable functions approximating the unity, which serves as the core tool from which we provide a nonlocal characterization of the Sobolev spaces and the space of functions of bounded variation via nonlocal energies forms. It turns out that this nonlocal …