On the first positive neumann eigenvalue

Wei Ming Ni; Xuefeng Wang

doi:10.3934/dcds.2007.17.1

On the first positive neumann eigenvalue

Wei Ming Ni, Xuefeng Wang

Mathematics

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8 Scopus citations

Abstract

We study the first positive Neumann eigenvalue μ₁ of the Laplace operator on a planar domain Ω. We are particularly interested in how the size of μ₁ depends on the size and geometry of Ω. A notion of the intrinsic diameter of Ω is proposed and various examples are provided to illustrate the effect of the intrinsic diameter and its interplay with the geometry of the domain.

Original language	English (US)
Pages (from-to)	1-19
Number of pages	19
Journal	Discrete and Continuous Dynamical Systems
Volume	17
Issue number	1
DOIs	https://doi.org/10.3934/dcds.2007.17.1
State	Published - Jan 2007

Keywords

Diffusion
Domain-monotonicity
First positive eigenvalue
Intrinsic diameter
Neumann eigenvalue problem

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KW - Intrinsic diameter

KW - Neumann eigenvalue problem

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On the first positive neumann eigenvalue

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Keywords

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