| Title: | Fractional Sobolev spaces with kernel function on compact Riemannian manifolds |
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| Authors: | ID Aberqi, Ahmed (Author)
ID Ouaziz, Abdesslam (Author)
ID Repovš, Dušan (Author) |
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| Files: |  URL - Source URL, visit https://link.springer.com/article/10.1007/s00009-023-02517-9
 PDF - Presentation file, download (507,44 KB)
MD5: 06566555FD00AC9F6D53E517044FD870
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| Language: | English |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: |  IMFM - Institute of Mathematics, Physics, and Mechanics
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| 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. |
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| Keywords: | nonlinear elliptic problem, fractional Sobolev spaces, kernel function, Lévy-integrability condition, compact Riemannian manifolds, existence of solutions, topological degree theory |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 01.01.2024 |
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| Year of publishing: | 2024 |
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| Number of pages: | 24 str. |
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| Numbering: | Vol. 21, iss. 1, article no. 6 |
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| PID: | 20.500.12556/DiRROS-18204  |
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| UDC: | 514.7 |
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| ISSN on article: | 1660-5446 |
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| DOI: | 10.1007/s00009-023-02517-9 |
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| COBISS.SI-ID: | 173366275 |
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| Note: |
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| Publication date in DiRROS: | 19.02.2024 |
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| Views: | 575 |
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| Downloads: | 230 |
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| Metadata: |    |
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