Stability with explicit constants of the critical points of the fractional Sobolev inequality and applications to fast diffusion

We study the quantitative stability of critical points fractional Sobolev inequality. show that, for a non-negative function u∈H˙s(RN) whose energy satisfies12SN,sN2s≤‖u‖H˙s(RN)≤32SN,sN2s, where SN,s is optimal constant, bound‖u−U[z,λ]‖H˙s(RN)≲‖(−Δ)su−u2s⁎−1‖H˙−s(RN), holds suitable Talenti bubble U[z,λ]. For functions u which are close to bubbles, we give sharp asymptotic value implied constant in this As an application this, derive explicit polynomial extinction rate positive solutions fast diffusion equation.