| Title: | On the concentration-compactness principle for anisotropic variable exponent Sobolev spaces and its applications |
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| Authors: | ID Chems Eddine, Nabil (Author)
ID Ragusa, Maria Alessandra (Author)
ID Repovš, Dušan (Author) |
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| Files: |  PDF - Presentation file, download (550,73 KB)
MD5: 1C7FEC19D9755EE00733A54E58C5A3A6
 URL - Source URL, visit https://link.springer.com/article/10.1007/s13540-024-00246-8
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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: | 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. |
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| Keywords: | Sobolev embeddings, concentration-compactness principle, anisotropic variable exponent Sobolev spaces, p(x)-Laplacian, fractional Brezis-Nirenberg problem |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 01.04.2024 |
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| Year of publishing: | 2024 |
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| Number of pages: | str. 725-756 |
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| Numbering: | Vol. 27, iss. 2 |
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| PID: | 20.500.12556/DiRROS-18484  |
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| UDC: | 517.9 |
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| ISSN on article: | 1311-0454 |
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| DOI: | 10.1007/s13540-024-00246-8 |
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| COBISS.SI-ID: | 186600963 |
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| Note: |
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| Publication date in DiRROS: | 20.03.2024 |
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| Views: | 291 |
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| Downloads: | 406 |
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