Fractional Sobolev spaces with kernel function on compact Riemannian manifolds
Analysis of PDEs
2023-11-28 v1 Functional Analysis
Abstract
In this paper, a new class of Sobolev spaces with kernel function satisfying a L\'evy-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 -Laplacian operator. As one of the main tools, topological degree theory is applied.
Cite
@article{arxiv.2311.15348,
title = {Fractional Sobolev spaces with kernel function on compact Riemannian manifolds},
author = {A. Aberqi and A. Ouaziz and D. D. Repovš},
journal= {arXiv preprint arXiv:2311.15348},
year = {2023}
}