A note on Kuttler–Sigillito’s inequalities

Asma Hassannezhad; Anna Siffert

doi:10.1007/s40316-019-00113-6

A note on Kuttler–Sigillito’s inequalities

Asma Hassannezhad
, Anna Siffert

School of Mathematics

Research output: Contribution to journal › Article (Academic Journal) › peer-review

9 Citations (Scopus)

242 Downloads (Pure)

Abstract

We provide several inequalities between eigenvalues of some classical eigenvalue problems on compact Riemannian manifolds with C² boundary. A key tool in the proof is the generalized Rellich identity on a Riemannian manifold. Our results in particular extend some inequalities due to Kuttler and Sigillito from subsets of R² to the manifold setting.

Original language	English
Number of pages	23
Journal	Annales mathématiques du Québec
Early online date	9 Mar 2019
DOIs	https://doi.org/10.1007/s40316-019-00113-6
Publication status	E-pub ahead of print - 9 Mar 2019

Keywords

Steklov eigenvalue problems
Eigenvalue bounds
Rellich identity

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10.1007/s40316-019-00113-6

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title = "A note on Kuttler–Sigillito{\textquoteright}s inequalities",

abstract = "We provide several inequalities between eigenvalues of some classical eigenvalue problems on compact Riemannian manifolds with C² boundary. A key tool in the proof is the generalized Rellich identity on a Riemannian manifold. Our results in particular extend some inequalities due to Kuttler and Sigillito from subsets of R² to the manifold setting.",

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AU - Siffert, Anna

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N2 - We provide several inequalities between eigenvalues of some classical eigenvalue problems on compact Riemannian manifolds with C² boundary. A key tool in the proof is the generalized Rellich identity on a Riemannian manifold. Our results in particular extend some inequalities due to Kuttler and Sigillito from subsets of R² to the manifold setting.

AB - We provide several inequalities between eigenvalues of some classical eigenvalue problems on compact Riemannian manifolds with C² boundary. A key tool in the proof is the generalized Rellich identity on a Riemannian manifold. Our results in particular extend some inequalities due to Kuttler and Sigillito from subsets of R² to the manifold setting.

KW - Steklov eigenvalue problems

KW - Eigenvalue bounds

KW - Rellich identity

U2 - 10.1007/s40316-019-00113-6

DO - 10.1007/s40316-019-00113-6

M3 - Article (Academic Journal)

SN - 2195-4755

JO - Annales mathématiques du Québec

JF - Annales mathématiques du Québec

ER -

A note on Kuttler–Sigillito’s inequalities

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Keywords

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