Inserted: 11 mar 2023
Journal: Partial Differential Equations and Applications
We introduce a class of concentrated p-Lévy integrable functions approximating the unity, which serves as the core tool to characterize the Sobolev spaces and the space of functions of bounded variation in the spirit of Bourgain-Brezis-Mironescu. We provide this characterization for a class of unbounded domains satisfying the extension property. We also examine the situation where the extension property fails.
Keywords: Sobolev spaces, nonlocal energies