On the first positive Neumann eigenvalue

Wei-Ming Ni; Xuefeng Wang

doi:10.3934/dcds.2007.17.1

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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: August 31, 2006

Published: December 2006

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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.

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Mathematics Subject Classification: 35P15, 35K05.

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