论文标题
负指数的Alt-Phillips功能最小化的紧凑型估计值
Compactness estimates for minimizers of the Alt-Phillips functional of negative exponents
论文作者
论文摘要
我们研究了alt-phillip的全局最小化器$ u \ ge 0 $功能的刚度涉及负功率电位的$$ \int_Ω\ left（| \ nabla u |^2 + U^2 + u^{ - γ}χ_ { $γ$接近可允许的值的极端。 特别是我们表明，如果$ \ {r}^n $中的全球最小化器是一维的，则如果$γ$接近2和$ n \ le 7 $，或者如果$γ$接近$ 0 $ $ 0 $和$ n \ le 4 $。
We investigate the rigidity of global minimizers $u \ge 0$ of the Alt-Phillips functional involving negative power potentials $$\int_Ω\left(|\nabla u|^2 + u^{-γ} χ_{\{u>0\}}\right) \, dx, \quad \quad γ\in (0,2),$$ when the exponent $γ$ is close to the extremes of the admissible values. In particular we show that global minimizers in $\mathbb{R}^n$ are one-dimensional if $γ$ is close to 2 and $n \le 7$, or if $γ$ is close to $0$ and $n \le 4$.
