Kuttler-Sigillito's Inequalities and Rellich-Christianson Identity

Stine Marie Berge

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arXiv · 2110.06801

Kuttler-Sigillito's Inequalities and Rellich-Christianson Identity

Stine Marie Berge

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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.

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Stine Marie Berge. 2021-10-13. Kuttler-Sigillito's Inequalities and Rellich-Christianson Identity. https://arxiv.org/abs/2110.06801

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