Sharp quantitative estimates of Struwe's Decomposition

Bin Deng, Liming Sun, Juncheng Wei

Suppose $u\in {\dot{H}}^1({\mathbb{R}}^n)$. In a seminal work, Struwe proved that if $u\ge 0$ and $\Vert \Delta u+u^{\frac{n+2}{n-2}}{\Vert }_{H^{-1}}:=\Gamma (u)\to 0$ then $dist(u,\mathcal{T})\to 0$, whe…