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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2605.03732 |
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| _version_ | 1866918484816953344 |
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| author | Fan, Song Li, Gui-Dong Zhang, Jianjun |
| author_facet | Fan, Song Li, Gui-Dong Zhang, Jianjun |
| contents | In this paper, we prove a sharp quantitative stability result for the affine fractional
\(L^2\)-Sobolev inequality in \(\dot H^s(\mathbb R^n)\), \(0<s<1\),
introduced by Haddad--Ludwig (\emph{Math. Ann.} \textbf{388} (2024), 1091--1115). In particular, we identify the kernel of the affine Hessian, determine the sharp local spectral gap, and show that the optimal global stability constant is strictly smaller than the corresponding local spectral value. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_03732 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Sharp Stability for the Affine Fractional Sobolev Inequality Fan, Song Li, Gui-Dong Zhang, Jianjun Analysis of PDEs 6E35, 26D10, 35R11 In this paper, we prove a sharp quantitative stability result for the affine fractional \(L^2\)-Sobolev inequality in \(\dot H^s(\mathbb R^n)\), \(0<s<1\), introduced by Haddad--Ludwig (\emph{Math. Ann.} \textbf{388} (2024), 1091--1115). In particular, we identify the kernel of the affine Hessian, determine the sharp local spectral gap, and show that the optimal global stability constant is strictly smaller than the corresponding local spectral value. |
| title | Sharp Stability for the Affine Fractional Sobolev Inequality |
| topic | Analysis of PDEs 6E35, 26D10, 35R11 |
| url | https://arxiv.org/abs/2605.03732 |