Fractional Sobolev logarithmic inequalities
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918329618268160 |
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| author | Sahu, Vivek |
| author_facet | Sahu, Vivek |
| contents | We establish new Euclidean Sobolev logarithmic inequalities in the framework of fractional Sobolev spaces and their weighted version. Our approach relies on a interpolation inequality, which can be viewed as a fractional Caffarelli-Kohn-Nirenberg type inequality. We further relate the optimal constant in this interpolation inequality to a corresponding variational problem. These results extend classical Sobolev logarithmic inequalities to the nonlocal Euclidean framework and provide new tools for analysis in fractional Sobolev spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_07559 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fractional Sobolev logarithmic inequalities Sahu, Vivek Analysis of PDEs 46E35, 26D15, 26A33 We establish new Euclidean Sobolev logarithmic inequalities in the framework of fractional Sobolev spaces and their weighted version. Our approach relies on a interpolation inequality, which can be viewed as a fractional Caffarelli-Kohn-Nirenberg type inequality. We further relate the optimal constant in this interpolation inequality to a corresponding variational problem. These results extend classical Sobolev logarithmic inequalities to the nonlocal Euclidean framework and provide new tools for analysis in fractional Sobolev spaces. |
| title | Fractional Sobolev logarithmic inequalities |
| topic | Analysis of PDEs 46E35, 26D15, 26A33 |
| url | https://arxiv.org/abs/2509.07559 |