Non-classical Eigenvalue Asymptotic for Elliptic Operators of Second Order in Unbounded Trumpet-shaped Domains with Neumann Boundary Conditions

Abstract

The paper deals with spectral properties of elliptic operators of second order in irregular unbounded domains with cusps. The eigenvalue asymptotic of the operator with Neumann boundary conditions is proved. The eigenvalue asymptotic in these domains is different from that with Dirichlet boundary conditions.