On the first positive neumann eigenvalue

Wei Ming Ni, Xuefeng Wang

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


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 languageEnglish (US)
Pages (from-to)1-19
Number of pages19
JournalDiscrete and Continuous Dynamical Systems
Issue number1
StatePublished - Jan 2007


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


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