Let Ω be a domain in R d with boundary Γ, Γ the Euclidean distance to and H = − div ( C ∇ ) an elliptic operator c k l > 0 where are real, bounded, Lipschitz functions. We assume that ∼ δ I as → sense of asymptotic analysis is strictly positive, function ≥ . also there r b , such weighted Hardy inequality ∫ | ψ 2 valid for all ∈ ∞ { x : < } then prove condition / sufficient essential self-adjoi...