On the first positive Neumann eigenvalue

Wei-Ming Ni; Xuefeng Wang

doi:10.3934/dcds.2007.17.1

Article Contents

2007, Volume 17, Issue 1: 1-19. Doi: 10.3934/dcds.2007.17.1

This issue Previous Article Next Article Two remarks on the generalised Korteweg de-Vries equation

On the first positive Neumann eigenvalue

Wei-Ming Ni^1, and
Xuefeng Wang^2,

1.
School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455
2.
Mathematics Department, Tulane University, New Orleans, LA 70118

Received: September 2006

Published: January 2007

Abstract Related Papers Cited by

Abstract

We study the first positive Neumann eigenvalue $\mu_1$ of the Laplace operator on a planar domain $\Omega$. We are particularly interested in how the size of $\mu_1$ depends on the size and geometry of $\Omega$. A notion of the intrinsic diameter of $\Omega$ is proposed and various examples are provided to illustrate the effect of the intrinsic diameter and its interplay with the geometry of the domain.

Keywords:

Mathematics Subject Classification: 35P15, 35K05.

Citation:

Article Metrics

HTML views() PDF downloads(419) Cited by(0)

On the first positive Neumann eigenvalue

Abstract

Access History

Article Metrics

Access History

Other Articles By Authors

Catalog

On the first positive Neumann eigenvalue

Abstract

Access History

SHARE

Article Metrics

Access History

Other Articles By Authors

Catalog

Export File

Citation

Format

Content