Kuttler-Sigillito's Inequalities and Rellich-Christianson Identity

2021/10/13 by Stine Marie Berge, Berge, Stine Marie · 1 citation
Materials Science · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Graph theory and applications #Quasicrystal Structures and Properties #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2110.06801

openalex publication_date 2021/10/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This article has two main objectives. The first one is to show Kuttler-Sigillito's type inequalities involving the mixed Neumann-Dirichlet, mixed Steklov-Dirichlet, and mixed Robin-Dirichlet eigenvalue problems. We will provide examples on e.g. squares and balls for the inequalities presented. Next we will show a Rellich identity for the mixed Neumann-Dirichlet problem. This identity will be used to prove a Rellich-Christianson identity for the Neumann-Dirichlet problem.

Cited by

• Biharmonic Steklov problems with Neumann boundary conditions and spectral inequalities on differential forms

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