In this talk, we consider anisotropic elliptic operators such as
where H and H∘ are polar Finsler norms on ℝN (N≥3) and -∞<λ≤(N-2)2∕4. When H(x)=|x|, where |x| denotes the euclidian norm on ℝN, operator Lλ,Hu becomes the classical Hardy-Sobolev operator-Δu-λ|x|2u. We completely classify the behavior near the origin for all positive weak solutions of Lλ,Hu=0 in {x∈ℝN:0<H∘(x)<1}. We establish that either u∕Φ+λ→γ+∈(0,∞) or u∕Φ-λ→γ-∈(0,∞), as |x|→0, where Φ±λ denote the fundamental solutions of Lλ,Hu=0. This is a joint work with F. Cîrstea.