Tuesday, January 26, 2021 - 14:15 in ZOOM - Video Conference
Fractional Orclicz-Sovolev spaces and their limits
A talk in the BI.discrete series by
Angela Alberico from IAC-CNR (Italy)
| Abstract: |
We establish versions for fractional Orlicz-Sobolev seminorms, built upon Young
functions, of the Bourgain-Brezis-Mironescu theorem on the limit as $s\rightarrow 1^-$, and
of the Maz’ya-Shaposhnikova theorem on the limit as $s\rightarrow 1^+$, dealing with classical
fractional Sobolev spaces. As regards the limit as $s\rightarrow 1^-$, Young functions with
an asymptotic linear growth are also considered in connection with the space of
functions of bounded variation. Concerning the limit as $s\rightarrow 1^+$, 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, Luboš Pick and Lenka Slavı́ková.
Zoom Meeting ID: 92653100938
Passcode: 1928
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