Fractional order Orlicz-Sobolev spaces

By Julián Fernández Bonder, Ariel Martin Salort. Journal of Functional Analysis, 2017

178 citations recorded by the source corpus.

In this paper we define the fractional order Orlicz-Sobolev spaces, and prove its convergence to the classical Orlicz-Sobolev spaces when the fractional parameter $s\uparrow 1$ in the spirit of the celebrated result of Bourgain-Brezis-Mironescu. We then deduce some consequences such as $\Gamma-$convergence of the modulars and convergence of solutions for some fractional versions of the $\Delta_g$ operator as the fractional parameter $s\uparrow 1$.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/dd71a776d81cd43d7ebf5d67edabb0568d5c7724

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In Applied Mathematics

1. Lenka Slav'ikov'a
2. L. Pick
3. Andrea Cianchi
4. A. Alberico
5. S. Bahrouni
6. L. S. Tavares
7. Hichem Ounaies
8. Iwona Chlebicka

In Geometry and Topology

1. L. Pick
2. Lenka Slav'ikov'a
3. Andrea Cianchi

Citations in the corpus

• Fractional Orlicz-Sobolev embeddings (2020, background): “equation (3.13) have been established FRACTIONAL ORLICZ-SOBOLEV EMBEDDINGS 9 in [11]. For functions Asatisfying the ∆2-condition and with the function Ain a somewhat implicit form, they are proved in [50]. The present general version can be found in [2]. We conclude this section with a fractional-or”
• Basic results of fractional Orlicz-Sobolev space and applications to non-local problems (2019, background): “As far as we know, the only results about the fractional Orlicz-Sobolev spaces and the fractional M -Laplacian are obtained in [7, 35].”