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Query: "keywords" (fractional Sobolev spaces) .

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1.
On the concentration-compactness principle for anisotropic variable exponent Sobolev spaces and its applications
Nabil Chems Eddine, Maria Alessandra Ragusa, Dušan Repovš, 2024, original scientific article

Abstract: We obtain critical embeddings and the concentration-compactness principle for the anisotropic variable exponent Sobolev spaces. As an application of these results,we confirm the existence of and find infinitely many nontrivial solutions for a class of nonlinear critical anisotropic elliptic equations involving variable exponents and two real parameters. With the groundwork laid in this work, there is potential for future extensions, particularly in extending the concentration-compactness principle to anisotropic fractional order Sobolev spaces with variable exponents in bounded domains. This extension could find applications in solving the generalized fractional Brezis–Nirenberg problem.
Keywords: Sobolev embeddings, concentration-compactness principle, anisotropic variable exponent Sobolev spaces, p(x)-Laplacian, fractional Brezis-Nirenberg problem
Published in DiRROS: 20.03.2024; Views: 291; Downloads: 406
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2.
Fractional Sobolev spaces with kernel function on compact Riemannian manifolds
Ahmed Aberqi, Abdesslam Ouaziz, Dušan Repovš, 2024, original scientific article

Abstract: 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.
Keywords: nonlinear elliptic problem, fractional Sobolev spaces, kernel function, Lévy-integrability condition, compact Riemannian manifolds, existence of solutions, topological degree theory
Published in DiRROS: 19.02.2024; Views: 161; Downloads: 58
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