5 papers · 1 filter
Symmetry, uniqueness and nondegeneracy of positive solutions of the Choquard equation
Song Fan, Gui-Dong Li, Jianjun Zhang
We study positive solutions \(Q\in H^1(\mathbb R^N)\) of \[-ΔQ+Q=(I_α*Q^p)Q^{p-1},\] where \(I_α\) is the Riesz potential of order \(α\), \(N\ge1\), \(0<α<N\), \(p>1+α/N\), and \((…
Sharp Quantitative Stability for the Affine -Sobolev Inequality, Part II: The Case
Song Fan, Gui-Dong Li, Jianjun Zhang
We prove a sharp quantitative stability result for the affine \(L^p\)-Sobolev inequality, for \(1<p<2\), introduced by Lutwak--Yang--Zhang (\emph{J. Differential Geom.}, \textbf{62…
Sharp Quantitative Stability for the Affine \(p\)-Sobolev Inequality, Part I: The Case \(2\le p<n\)
Song Fan, Gui-Dong Li, Jianjun Zhang
We prove a sharp quantitative stability result for the affine \(L^p\)-Sobolev inequality, for \(p\ge2\), introduced by Lutwak--Yang--Zhang (\emph{J. Differential Geom.}, \textbf{62…
Sharp Stability for the Affine Fractional Sobolev Inequality
Song Fan, Gui-Dong Li, Jianjun Zhang
In this paper, we prove a sharp quantitative stability result for the affine fractional \(L^2\)-Sobolev inequality in \(\dot H^s(\mathbb R^n)\), \(0<s<1\), introduced by Haddad--Lu…
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\i…