On the concentration-compactness principle for anisotropic variable exponent Sobolev spaces and its applications
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| Main Authors: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866929289264365568 |
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| author | Eddine, N. Chems Ragusa, M. A. Repovš, D. D. |
| author_facet | Eddine, N. Chems Ragusa, M. A. Repovš, D. D. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2402_15133 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the concentration-compactness principle for anisotropic variable exponent Sobolev spaces and its applications Eddine, N. Chems Ragusa, M. A. Repovš, D. D. Analysis of PDEs Functional Analysis 35B33, 35D30, 35J20, 35J60, 46E35 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. |
| title | On the concentration-compactness principle for anisotropic variable exponent Sobolev spaces and its applications |
| topic | Analysis of PDEs Functional Analysis 35B33, 35D30, 35J20, 35J60, 46E35 |
| url | https://arxiv.org/abs/2402.15133 |