The spectrum of large powers of the Laplacian in bounded domains

Details The spectrum of large powers of the Laplacian in bounded domains The spectrum of large powers of the Laplacian in bounded domains

2007-11-15

arxiv.org/abs/0711.2518v1

J. Phys. A: Math. Theor. 41 (2008) 022002

Physics

Condensed Matter

Statistical Mechanics

13 pages, 2 figures

Scientific paper

10.1088/1751-8113/41/2/022002

We present exact results for the spectrum of the Nth power of the Laplacian in a bounded domain. We begin with the one dimensional case and show that the whole spectrum can be obtained in the limit of large N. We also show that it is a useful numerical approach valid for any N. Finally, we discuss implications of this work and present its possible extensions for non integer N and for 3D Laplacian problems.

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