论文标题
Sobolev不等式的尖锐梯度稳定性
Sharp gradient stability for the Sobolev inequality
论文作者
论文摘要
我们证明了$ p $ -sobolev的不等式的任何$ 1 <p <n $的尖锐定量版本，并且可以控制与最佳功能类别的最强距离。出人意料的是，$ p <2 $的尖锐指数是恒定的，而$ p $ $ p> $ p> 2 $。
We prove a sharp quantitative version of the $p$-Sobolev inequality for any $1<p<n$, with a control on the strongest possible distance from the class of optimal functions. Surprisingly, the sharp exponent is constant for $p<2$, while it depends on $p$ for $p>2$.
