Eigenvalues of the negative Laplacian for arbitrary multiply connected domains

Abstract

The purpose of this paper is to derive some interesting asymptotic formulae for spectra of arbitrary multiply connected bounded domains in two or three dimensions, linked with variation of positive distinct functions entering the boundary conditions, using the spectral function ∑k=1∞{μk(σ1,…,σn)+P}−2 as P→∞. Further results may be obtained.

Keywords

• inverse problem
• negative Laplacian
• eigenvalues
• spectral functions.