Stability estimate for the Lane–Emden inequality

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发表日期：

2025年8月23日

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Eric Carlen,
Mathieu Lewin,
Elliott H. Lieb,
Robert Seiringer

摘要

The Lane–Emden inequality controls \(\iint _{\mathbb {R}^{2d}}\rho (x)\rho (y)|x-y|^{-\lambda }\,\textrm{d}x\,\textrm{d}y\) in terms of the \(L^1\) and \(L^p\) norms of \(\rho \) . We provide a remainder estimate for this inequality in terms of a suitable distance of \(\rho \) to the manifold of optimizers.