论文标题
泳道基层状态的正常衍生物的不平等
An inequality for the normal derivative of the Lane-Emden ground state
论文作者
论文摘要
我们考虑具有多极体指数$ 0 \ leq Q-1 \ leq 1 $的车道填充地面状态，也就是说，在$ l^q $ normalized函数中，dirichlet积分的最小化。我们的主要结果是在能量方面对正常衍生物的$ l^2 $ norm有一个尖锐的下限，这意味着相应的等速度不平等。我们的界限适用于任意有限的开放lipschitz设置$ω\ subset \ mathbb {r}^d $，而无需假设凸度。
We consider Lane-Emden ground states with polytropic index $0\leq q-1\leq 1$, that is, minimizers of the Dirichlet integral among $L^q$-normalized functions. Our main result is a sharp lower bound on the $L^2$-norm of the normal derivative in terms of the energy, which implies a corresponding isoperimetric inequality. Our bound holds for arbitrary bounded open Lipschitz sets $Ω\subset\mathbb{R}^d$, without assuming convexity.
