The spectrum of large powers of the Laplacian in bounded domains

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.

💡 Research Summary

The paper addresses the spectral problem for the N‑th power of the Laplacian operator, Δⁿ, on bounded domains. It begins with a rigorous analytical treatment of the one‑dimensional interval