论文标题
$ \ mathbb {r}^2 $中半稳定解决方案的关键点的唯一性
Uniqueness of the critical point for semi-stable solution in $\mathbb{R}^2$
论文作者
论文摘要
在本文中，我们显示了问题的\ emph {semi -stable}解决方案的关键点的独特性$ω\ subset \ mathbb {r}^2 $是一个平滑的有限域，其边界具有\ emph {nonnegative}曲率和$ f（0）\ ge0 $。它将Cabré-Chanillo的结果扩展到了$ \partialΩ$消失的情况下。
In this paper we show the uniqueness of the critical point for \emph{semi-stable} solutions of the problem $$\begin{cases} -Δu=f(u)&\text{in }Ω\\ u>0&\text{in }Ω\\ u=0&\text{on } \partialΩ,\end{cases}$$ where $Ω\subset\mathbb{R}^2$ is a smooth bounded domain whose boundary has \emph{nonnegative} curvature and $f(0)\ge0$. It extends a result by Cabré-Chanillo to the case where the curvature of $\partialΩ$ vanishes.
