Eigenvalues of the Negative Laplacian for Simply Connected Bounded Domains

This paper is devoted to asymptotic formulae for functions related with the spectrum of the negative Laplacian in two and three dimensional bounded simply connected domains with impedance boundary conditions, where the impedances are assumed to be discontinuous functions. Moreover, asymptotic expressions for the difference of eigenvalues related to the impedance problems with different impedances are derived. Further results may be obtained.