论文标题
稳定性，具有分数Sobolev不平等的临界点的明确常数和快速扩散的应用
Stability with explicit constants of the critical points of the fractional Sobolev inequality and applications to fast diffusion
论文作者
论文摘要
我们研究了sobolev不平等的临界点的定量稳定性。我们表明，对于非阴性函数$ u \ in \ dot h^s（\ mathbb r^n）$，其能量满足$$ \ tfrac {1} {2} {2} s^\ frac {n} n} {2S} {2S} {2S} _ { \ tfrac {3} {2} s_ {n，s}^\ frac {n} {n} {2s}，$$其中$ s_ {n，s} $是最佳sobolev常数，bound $ \ | u -u -u -u -u -u -u -u -u -u -u -e [z，λ] \ |（-δ） {对于接近Talenti Bubbles的函数$ U $，我们给出了这种不平等中隐含常数的急剧渐近价值。}作为应用程序{}的应用{}，我们得出了对分数快速扩散方程的正溶液的显式多项式灭绝率。
We study the quantitative stability of critical points of the fractional Sobolev inequality. We show that, for a non-negative function $u \in \dot H^s(\mathbb R^N)$ whose energy satisfies $$\tfrac{1}{2} S^\frac{N}{2s}_{N,s} \le \|u\|_{\dot H^s(\mathbb R^N)} \le \tfrac{3}{2}S_{N,s}^\frac{N}{2s},$$ where $S_{N,s}$ is the optimal Sobolev constant, the bound $$ \|u -U[z,λ]\|_{\dot{H}^s(\mathbb R^N)} \lesssim \|(-Δ)^s u - u^{2^*_s-1}\|_{\dot{H}^{-s}(\mathbb R^N)}, $$ holds for a suitable fractional Talenti bubble $U[z,λ]$. {For functions $u$ which are close to Talenti bubbles, we give the sharp asymptotic value of the implied constant in this inequality.} As an application {of this}, we derive an explicit polynomial extinction rate for positive solutions to a fractional fast diffusion equation.
