On a new fractional Sobolev space with variable exponent on complete manifolds

Aberqi, Ahmed (author), Benslimane, Omar (author), Ouaziz, Abdesslam (author), Repovš, Dušan (author)

We present the theory of a new fractional Sobolev space in complete manifolds with variable exponent. As a result, we investigate some of our new space’s qualitative properties, such as completeness, reflexivity, separability, and density. We also show that continuous and compact embedding results are valid. We apply the conclusions of this study to the variational analysis of a class of fractional $p(z, \cdot)$-Laplacian problems involving potentials with vanishing behavior at infinity as an application.

• Language: English
• Keywords: fractional ▫$p(z, \cdot)$▫-Laplacian, existence of solutions, fractional Sobolev space with variable exponent on complete manifolds, variational method
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Year: 2022
• Number of pages: 20 str.
• Numbering: Vol. 2022, art. 7
• PID: 20.500.12556/RUL-135275
• UDC: 517.956
• ISSN on article: 1687-2770
• DOI: 10.1186/s13661-022-01590-5
• COBISS.SI-ID: 96892419
• Publication date in RUL: 04.03.2022

Record is a part of a journal

• Title: Boundary value problems
• Shortened title: Bound. value probl.
• Publisher: Springer
• ISSN: 1687-2770
• COBISS.SI-ID: 62113025

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.