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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
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
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

〈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

(−1)jDj (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.

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