We study a characterization of BV and Sobolev functions via nonlocal functionals in metric spaces equipped with a doubling measure and supporting a Poincaré 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 functionals is only comparable, not necessarily equal, to the variation measure ‖Df‖(Ω).
A characterization of BV and Sobolev functions via nonlocal functionals in metric spaces / Lahti, P.; Pinamonti, A.; Zhou, X.. - In: NONLINEAR ANALYSIS. - ISSN 0362-546X. - 241:(2024). [10.1016/j.na.2023.113467]
A characterization of BV and Sobolev functions via nonlocal functionals in metric spaces
Pinamonti A.
;
2024-01-01
Abstract
We study a characterization of BV and Sobolev functions via nonlocal functionals in metric spaces equipped with a doubling measure and supporting a Poincaré 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 functionals is only comparable, not necessarily equal, to the variation measure ‖Df‖(Ω).I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione
