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) |
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Pages (from-to) | 1-19 |
Number of pages | 19 |
Journal | Discrete and Continuous Dynamical Systems |
Volume | 17 |
Issue number | 1 |
DOIs | |
State | Published - Jan 2007 |
Keywords
- Diffusion
- Domain-monotonicity
- First positive eigenvalue
- Intrinsic diameter
- Neumann eigenvalue problem