Calculus of Variations and Geometric Measure Theory

A. Hassannezhad - A. Siffert

A note on Kuttler-Sigillito's inequalities

created by hassannezhad1 on 04 Dec 2020



Inserted: 4 dec 2020

Year: 2017

ArXiv: 1709.09841 PDF


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.