Calculus of Variations and Geometric Measure Theory

G. Foghem

Nonlocal characterization of Sobolev spaces

created by foghem on 11 Mar 2023


Published Paper

Inserted: 11 mar 2023

Journal: Partial Differential Equations and Applications
Pages: 27
Year: 2023
Doi: 10.1007/s42985-023-00232-4

ArXiv: PDF


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