Eigenvalue Asymptotics for the Non-Selfadjoint Operator Induced by a Parameter-Elliptic Multi-Order Boundary Problem

摘要

In this paper we consider a boundary problem for a parameter-elliptic, multi-order system of differential equations defined over a bounded region in ${mathbb{R}^n}$ and under Dirichlet boundary conditions. In addition, the problem is considered under limited smoothness assumptions. Information is then derived concerning the asymptotic behaviour of the eigenvalues of the Hilbert space operator, in general non-selfadjoint, induced by the boundary problem under null boundary conditions.