Journal article
Laplace eigenvalues on regular polygons: A series in 1 / N
Journal of mathematical analysis and applications, v 385(1)
2012
Abstract
For regular polygons
P
N
inscribed in a circle, the eigenvalues of the Laplacian converge as
N
→
∞
to the known eigenvalues on a circle. We compute the leading terms of
λ
N
/
λ
in a series in powers of
1
/
N
, by applying the calculus of moving surfaces to a piecewise smooth evolution from the circle to the polygon. The
O
(
1
/
N
2
)
term comes from Hadamardʼs formula, and reflects the change in area. This term disappears if we “transcribe” the polygon, scaling it to have the same area as the circle.
Metrics
Details
- Title
- Laplace eigenvalues on regular polygons: A series in 1 / N
- Creators
- Pavel Grinfeld - Drexel UniversityGilbert Strang - Massachusetts Institute of Technology
- Publication Details
- Journal of mathematical analysis and applications, v 385(1)
- Publisher
- Elsevier
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000294979100014
- Scopus ID
- 2-s2.0-80051791256
- Other Identifier
- 991019312386904721
InCites Highlights
Data related to this publication, from InCites Benchmarking & Analytics tool:
- Collaboration types
- Domestic collaboration
- Web of Science research areas
- Mathematics
- Mathematics, Applied