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arXiv · 2410.20113

Stability estimate for the Lane-Emden inequality

Eric Carlen·Mathieu Lewin·Elliott H. Lieb·Robert Seiringer
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Abstract

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.

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Eric Carlen, Mathieu Lewin, Elliott H. Lieb, Robert Seiringer. 2024-10-26. Stability estimate for the Lane-Emden inequality. https://doi.org/10.1007/s00526-025-03062-x

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