Elliptic Problems Involving an Indefinite Weight Function
M. Faierman, Heinz Langer · Birkhäuser Basel eBooks · 1996
We consider an elliptic boundary value problem defined on a region Ω ⊂ ℝn and involving an indefinite weight function ω. We also suppose that the problem under consideration admits a variational formulation. Then by appealing to the theory of selfadjoint operators acting in a Krein space, we derive various spectral properties for the problem. In particular, when Ω is bounded we show that the principal vectors of our problem form a Riesz basis in L 2(Ω†; |ω(x)|dx), where Ω† = {x ∈ Ω|ω(x) ≠ 0}, and also establish some results concerning their half-range completeness.