关于Kuttler-Sigillito不等式的注记
A note on Kuttler-Sigillito's inequalities
摘要：
给出了完备黎曼流形中具有$C^2$边界区域上某些经典本征值问题的特征值之间的几个不等式.证明中的一个关键工具是黎曼流形上的广义Rellich恒等式。我们的结果特别是扩展了一些不等式由于Kutller和Sigillito从子集的$\mathbb{R}^2$的流形设置。
英文摘要：
We provide several inequalities between eigenvalues of some classical eigenvalue problems on domains with $C^2$ boundary in complete Riemannian manifolds. A key tool in the proof is the generalized Rellich identity on a Riemannian manifold. Our results in particular extend some inequalities due to Kutller and Sigillito from subsets of $\mathbb{R}^2$ to the manifold setting.
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