On the resolvent arising in a parameter‐elliptic multi‐order boundary problem |
| |
Authors: | M Faierman |
| |
Institution: | School of Mathematics and Statistics, The University of New South Wales, UNSW Sydney, NSW 2052, Australia |
| |
Abstract: | 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 limited smoothness assumptions as well as under boundary conditions which include those of Dirichlet. Information is then derived concerning the asymptotic behaviour of the trace of a power of the resolvent of the Hilbert space operator, in general non‐selfadjoint, induced by the boundary problem under null boundary conditions. This information will then be used in a subsequent work to derive various results pertaining to the asymptotic behaviour of the eigenvalues of this operator. |
| |
Keywords: | Parameter‐elliptic multi‐order resolvent asymptotics msc (2010) 35P99 47F05 |
|
|