Abstract
AbstractIn 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 $$p(\cdot , \cdot )$$
p
(
·
,
·
)
-Laplacian operator. As one of the main tools, topological degree theory is applied.
Funder
Javna Agencija za Raziskovalno Dejavnost RS
Publisher
Springer Science and Business Media LLC
Reference36 articles.
1. Aberqi, A., Bennouna, J., Benslimane, O., Ragusa, M.A.: Existence results for double phase problem in Sobolev–Orlicz spaces with variable exponents in complete manifold. Mediterr. J. Math. 19(4), 158 (2022)
2. Aberqi, A., Benslimane, O., Ouaziz, A., Repovš, D.D.: On a new fractional Sobolev space with variable exponent on complete manifolds. Bound. Value Probl. 2022(1), 7 (2022)
3. Adams, R.A., Fournier, J.J.: Sobolev Spaces. Elsevier, Amsterdam (2003)
4. Applebaum, D.: Lévy processes - from probability to finance and quantum groups. Not. Am. Math. Soc. 51(11), 1336–1347 (2004)
5. Aubin, T.: Nonlinear Analysis on Manifolds. Monge–Ampere Equations, vol. 252. Springer Science & Business Media, Berlin (2012)