functional inequalities 2affine analysis 1affine Sobolev inequality 1fractional sobolev inequalities 1optimal exponent 1quantitative stability 1sharp constants 1spectral gap 1stability estimates 1
From the 2 of 3 linked papers with an AI index.
3 papers
math.AP2026
Sharp Quantitative Stability for the Affine \(p\)-Sobolev Inequality, Part I: The Case \(2\le p<n\)
Song Fan, Gui-Dong Li, Jianjun Zhang
The authors establish a sharp quantitative stability theorem for the affine L^p‑Sobolev inequality in the range 2 ≤ p < n, proving that the stability exponent is exactly p and cann…
math.AP2026
Sharp Stability for the Affine Fractional Sobolev Inequality
Song Fan, Gui-Dong Li, Jianjun Zhang
The paper proves a precise quantitative stability result for an affine fractional Sobolev inequality, identifying key spectral properties and showing the optimal global stability c…
math.AP2026
Stability of the Sobolev--Escobar bridge inequality
Fan Song, Li Gui-Dong, Zhang Jianjun
We study the local stability of the bridge family \[ Φ(T):=\inf_{u\in\mathcal A_T}\|\nabla u\|_{L^2(\mathbb R^n_+)}, \qquad T>0,\quad n\ge3, \] where \[ \mathcal A_T := \Bigl\{ u\…