Singular subelliptic equations and Sobolev inequalities on nilpotent Lie groups

In this article we study singular subelliptic p-Laplace equations and best constants in Sobolev inequalities on nilpotent Lie groups. We prove solvability of these subelliptic p-Laplace equations and existence of the minimizer of the corresponding variational problem. It leads to existence of the best constant in the corresponding (q, p)-Sobolev inequality, 0 < q < 1, 1 < p < ν.