Abstract
We establish versions for fractional Orlicz-Sobolev seminorms, built upon Young
functions, of the Bourgain-Brezis-Mironescu theorem on the limit as s->1^-, and of the Maz'ya-Shaposhnikova theorem on the limit as
s-> 0^+ ,
dealing with classical fractional Sobolev spaces. As regards the limit as s->1^-,
Young functions with an asymptotic linear growth are also considered in connection
with the space of functions of bounded variation. Concerning the limit as s-> 0^+,
Young functions fulfilling the \Delta_2-condition are admissible. Indeed, counterexamples
show that our result may fail if this condition is dropped. This is a joint work with
Andrea Cianchi, Lubos Pick and Lenka Slavikova.
Anno
2021
Autori IAC
Tipo pubblicazione
Altri Autori
Angela Al berico