Anisotropic elliptic problems involving Hardy-type potentials

In this paper, we give existence, uniqueness and regularity of the solutions of problems whose prototype is { − Δ H u = λ H o ( x ) 2 u + f ( x ) in  Ω , u = 0 on  ∂ Ω , where Ω is a bounded open set of R N , N > 2 , and 0 ∈ Ω . Here H is a norm on R N , H o is its polar and Δ H u = div ( H ( D u ) H ξ ( D u ) ) is the anisotropic Laplacian.