Weighted Hardy's inequalities and the variational problem with compact perturbations

Let Ω be a bounded domain of ℝN (N ≥ 1) whose boundary ∂Ω is a C2 compact manifolds. In the present paper we shall study a variational problem relating the weighted Hardy inequalities established in [4]. As weights we adopt powers of the distance function 𝛿(x) to the boundary ∂Ω.