Noncritical Weighted Hardy's Inequalities with compact perturbations

Let $Ω$ be a bounded domain of $\mathbb{R}^N$ whose boundary is a $\mathbb{C}^2$ compact manifolds. In the present paper we shall study a variational problem relating the weighted Hardy inequalities with sharp missing terms. As weights we adopted powers of the distance function $δ(x)$ to the boundary $\partialΩ$.

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