IPM
30
YEARS OLD

## “School of Mathematics”

Paper   IPM / M / 179
School of Mathematics
Title: On the spectral properties of generalized non self-adjoint elliptic systems of differential operators degenerated on the boundary of domain
Author(s):
 1 . A. Sameripour 2 . K. Seddighi
Status: Published
Journal: Bull. Iranian Math. Soc.
No.: 1
Vol.: 24
Year: 1998
Pages: 15-32
Supported by: IPM
Abstract:
Let Ω ⊂ Rn be a bounded domain with smooth boundary i.e. ∂Ω ∈ C. In this paper we consider the non-selfadjoint operator A on the space Hl=L2(Ω)l=L2(Ω)l ×…×L2(Ω) (l-times) associated with the noncoercive bilinear form
 A[u,v]= ⌠⌡ Ω 〈ρα (x) a(x) q(x) Di u (x), ρα (x) Dj u(x)〉Cl dx,
where D[A]=W°2,αn(Ω)l is the domain of the bilinear form associated with the operator A defined by
 (Au)(x)= n∑ i,j=1 (−1)jDj (ρ2α (x) aij (x)q(x) Di u(x)),
with the Dirichlet-type boundary conditions, here ρ(x)=dist{x,∂Ω}, 0 ≤ α < 1, aij(x) ∈ C2(Ω), aij=aji, |s| ≤ MΣi,j=1n aij (x) sisj (x ∈ Ω, sCn), the matrix q(x) has distinct eigenvalues contained in the sector Φ = {zC:|argz| ≤ φ}, φ ∈ (0,π). We will find the resolvent and some other spectral properties of A.