20.500.12556/RUL-152540 Fractional Sobolev spaces with kernel function on compact Riemannian manifolds 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. nonlinear elliptic problem fractional Sobolev spaces kernel function Lévy-integrability condition compact Riemannian manifolds existence of solutions topological degree theory true false true Angleški jezik Ni določen Članek v reviji 2023-11-27 10:02:45 2023-11-27 10:02:47 2024-03-08 11:13:20 0000-00-00 00:00:00 2024 0 0 24 str. iss. 1, art. 6 Vol. 21 2024 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 514.7 1660-5446 10.1007/s00009-023-02517-9 173366275 RAZ_Aberqi_Ahmed_2024.pdf RAZ_Aberqi_Ahmed_2024.pdf 1 ECB357D3C0A56CABE5F93F69B290CE79 9616cf3dcfbb4091b41f2b2c68b43c40a6677645f3970c97ae6324f732ca01c7 85f61547-8d04-11ee-8ac8-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=178064 https://link.springer.com/article/10.1007/s00009-023-02517-9 1 bd3088d5-8d03-11ee-8ac8-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=178063 Pedagoška fakulteta Fakulteta za matematiko in fiziko 0 0 0