Accepted Paper

Inserted: 5 jul 2022
Last Updated: 12 dec 2023

Journal: Nonlinear Analysis
Year: 2022

Abstract:

We study a characterization of BV and Sobolev functions via nonlocal functionals in metric spaces equipped with a doubling measure and supporting a Poincar\'e inequality. Compared with previous works, we consider more general functionals. We also give a counterexample in the case $p=1$ demonstrating that unlike in Euclidean spaces, in metric measure spaces the limit of the nonlocal functions is only comparable, not necessarily equal, to the variation measure $\Vert Df\Vert(\Omega)$.

Download:

• DavilaPropertyMetric17.pdf