Eigenvalue distribution of elliptic operators of second order in domains with infinitely many hooks

Abstract

Spectral properties of strongly elliptic operators of second order on bounded domains with infinitely many hooks and Neumann boundary conditions are considered. In the case of a pure point spectrum asymptotic formulae with remainder estimates for the counting function N(λ) of the eigenvalues are proved. These formulae yield the conclusion that the asymptotic eigenvalue distributions coincide with the classical formula of Weyl.