We compute best constants in functional inequalities which we call Rellich-Hardy inequalities for solenoidal vector fields on \(\mathbb {R}^N\) ; this gives a solenoidal improvement of the inequalities whose best constants are known for unconstrained fields. We give a stronger version of Rellich-Leray inequality studied in our previous work (Hamamoto in Calc Var Partial Differ Equ 60:65, 2021). In order to compute the best constants including any radial power weight, we will show the non-negativity of many polynomial functions of even degree by straightforward numerical calculations with some ingenuity.
