Calculus of Variations and Geometric Measure Theory
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M. Capolli - A. Maione - A. M. Salort - E. Vecchi

Asymptotic behaviours in Fractional Orlicz-Sobolev spaces on Carnot groups

created by maione on 19 Dec 2019
modified on 05 Mar 2021


Published Paper

Inserted: 19 dec 2019
Last Updated: 5 mar 2021

Journal: The Journal of Geometric Analysis
Volume: 31
Number: 3
Pages: 3196-3229
Year: 2021
Doi: 10.1007/s12220-020-00391-5

ArXiv: 1912.08357 PDF


In this article we define a class of fractional Orlicz-Sobolev spaces on Carnot groups and, in the spirit of the celebrated results of Bourgain-Brezis-Mironescu and of Maz'ya-Shaposhnikova, we study the asymptotic behavior of the Orlicz functionals when the fractional parameter goes to $1$ and $0$.

Keywords: Carnot groups, Orlicz spaces, Asymptotic behaviours, Fractional Sobolev norms

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