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Fractional Sobolev spaces with kernel function on compact Riemannian manifoldsAhmed Aberqi,
Abdesslam Ouaziz,
Dušan Repovš, 2024, izvirni znanstveni članek
Povzetek: 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.
Ključne besede: nonlinear elliptic problem, fractional Sobolev spaces, kernel function, Lévy-integrability condition, compact Riemannian manifolds, existence of solutions, topological degree theory
Objavljeno v DiRROS: 19.02.2024; Ogledov: 147; Prenosov: 54
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