Uniqueness of Extremizers and Convergence of the Euler-Lagrange Iteration for the Critical Hardy-Littlewood-Sobolev Inequality

Hanwen Lu

Let $n\ge 3$, $2\le \alpha <n$, and $1<p,r<\infty$ satisfy $p^{-1}+r^{-1}=1+\alpha /n$. We prove uniqueness, up to common translations and dilations, of the normalized nonnegative extre…