Stability estimate for the Lane-Emden inequality
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917149422911488 |
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| author | Carlen, Eric Lewin, Mathieu Lieb, Elliott H. Seiringer, Robert |
| author_facet | Carlen, Eric Lewin, Mathieu Lieb, Elliott H. Seiringer, Robert |
| contents | The Lane-Emden inequality controls $\iint_{\mathbb{R}^{2d}}ρ(x)ρ(y)|x-y|^{-λ}\,dx\,dy$ in terms of the $L^1$ and $L^p$ norms of $ρ$. We provide a remainder estimate for this inequality in terms of a suitable distance of $ρ$ to the manifold of optimizers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_20113 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stability estimate for the Lane-Emden inequality Carlen, Eric Lewin, Mathieu Lieb, Elliott H. Seiringer, Robert Analysis of PDEs Mathematical Physics The Lane-Emden inequality controls $\iint_{\mathbb{R}^{2d}}ρ(x)ρ(y)|x-y|^{-λ}\,dx\,dy$ in terms of the $L^1$ and $L^p$ norms of $ρ$. We provide a remainder estimate for this inequality in terms of a suitable distance of $ρ$ to the manifold of optimizers. |
| title | Stability estimate for the Lane-Emden inequality |
| topic | Analysis of PDEs Mathematical Physics |
| url | https://arxiv.org/abs/2410.20113 |