Fractional Sobolev spaces with kernel function on compact Riemannian manifolds

Aberqi, Ahmed (avtor), Ouaziz, Abdesslam (avtor), Repovš, Dušan (avtor)

In this paper, a new class of Sobolev spaces with kernel function satisfying a Lévy-integrability-type condition on compact Riemannian manifolds is presented. We establish the properties of separability, reflexivity, and completeness. An embedding result is also proved. As an application, we prove the existence of solutions for a nonlocal elliptic problem involving the fractional $p(\cdot, \cdot)$-Laplacian operator. As one of the main tools, topological degree theory is applied.

• Jezik: Angleški jezik
• Ključne besede: nonlinear elliptic problem, fractional Sobolev spaces, kernel function, Lévy-integrability condition, compact Riemannian manifolds, existence of solutions, topological degree theory
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: PEF - Pedagoška fakulteta; FMF - Fakulteta za matematiko in fiziko
• Status publikacije: Objavljeno
• Različica publikacije: Objavljena publikacija
• Leto izida: 2024
• Št. strani: 24 str.
• Številčenje: Vol. 21, iss. 1, art. 6
• PID: 20.500.12556/RUL-152540
• UDK: 514.7
• ISSN pri članku: 1660-5446
• DOI: 10.1007/s00009-023-02517-9
• COBISS.SI-ID: 173366275
• Datum objave v RUL: 27.11.2023

Gradivo je del revije

• Naslov: Mediterranean journal of mathematics
• Skrajšan naslov: Mediterr. j. math.
• Založnik: Springer Nature, University of Bari, Department of Mathematics
• ISSN: 1660-5446
• COBISS.SI-ID: 13561433

Licence

• Licenca: CC BY 4.0, Creative Commons Priznanje avtorstva 4.0 Mednarodna
• Povezava: http://creativecommons.org/licenses/by/4.0/deed.sl
• Opis: To je standardna licenca Creative Commons, ki daje uporabnikom največ možnosti za nadaljnjo uporabo dela, pri čemer morajo navesti avtorja.