Stability estimate for the Lane-Emden inequality

2024/10/26 by Eric A. Carlen, Mathieu Lewin, Carlen, Eric +5 · 1 citation
Mathematics · #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Differential Equations Analysis #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2410.20113

openalex publication_date 2024/10/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The Lane-Emden inequality controls \iint_ℝ^2dρ(x)ρ(y)|x-y|^-λ dx dy in terms of the L¹ 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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