论文标题
罗宾问题解决方案的凹陷特性
Concavity properties of solutions to Robin problems
论文作者
论文摘要
我们证明，罗宾的基态和罗宾扭转功能分别是对数concave和$ \ frac {1} {2} {2} $ - 在均匀凸出域$ω\ subset \ subset \ subset \ subset \ subset \ subset \ subset \ mathbb {r}^n $ class $ \ mathcal {c}^m $的c} 4 $，前提是罗宾参数超过关键阈值。这种阈值取决于$ n $，$ m $和$ω$的几何形状，恰恰在直径和边界曲率上，直到订购$ m $。
We prove that the Robin ground state and the Robin torsion function are respectively log-concave and $\frac{1}{2}$-concave on an uniformly convex domain $Ω\subset \mathbb{R}^N$ of class $\mathcal{C}^m$, with $[m -\frac{ N}{2}]\geq 4$, provided the Robin parameter exceeds a critical threshold. Such threshold depends on $N$, $m$, and on the geometry of $Ω$, precisely on the diameter and on the boundary curvatures up to order $m$.
