On best constants in Hardy inequalities with a remainder term Original Research Article

Let ΩΩ be a bounded open set of RNRN containing the origin. We compute the best value of the constant C(α,|Ω|)C(α,|Ω|) in View the MathML source∫Ω|∇u|2dx−(N−2)42∫Ωu2|x|2dx≥C(α,|Ω|)‖u‖L(2NN−α,2)2, Turn MathJax on with α<2α<2 and View the MathML sourceu∈H01(Ω). Then we get the optimal value of C(|Ω|)C(|Ω|) in