Stability estimate for the Lane-Emden inequality

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.

💡 Research Summary

The paper addresses a quantitative refinement of the classical Lane‑Emden inequality, which bounds the double integral
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