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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.04064 |
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| _version_ | 1866909567110086656 |
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| author | Gonzalez, Maria del Mar Hyder, Ali Saez, Mariel |
| author_facet | Gonzalez, Maria del Mar Hyder, Ali Saez, Mariel |
| contents | In this paper we study the fractional Caffarelli-Kohn-Nirenberg inequality (CKN) in one dimension when the parameter $γ$ converges (from the left) to its critical value $1/2$, obtaining Onofri's inequality in the unit disk as the limit. A difficulty that we encounter is the lack of an explicit expression for the extremal function at which the CKN inequality is attained, which we address by studying solutions of the weighted Liouville equation for the half-Laplacian in dimension one. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_04064 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The limiting case of the fractional Caffarelli-Kohn-Nirenberg inequality in dimension one Gonzalez, Maria del Mar Hyder, Ali Saez, Mariel Analysis of PDEs In this paper we study the fractional Caffarelli-Kohn-Nirenberg inequality (CKN) in one dimension when the parameter $γ$ converges (from the left) to its critical value $1/2$, obtaining Onofri's inequality in the unit disk as the limit. A difficulty that we encounter is the lack of an explicit expression for the extremal function at which the CKN inequality is attained, which we address by studying solutions of the weighted Liouville equation for the half-Laplacian in dimension one. |
| title | The limiting case of the fractional Caffarelli-Kohn-Nirenberg inequality in dimension one |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2504.04064 |