Optimal decay of p-Sobolev extremals on Carnot groups

Abstract

We determine the sharp asymptotic behavior at infinity of solutions to quasilinear critical problems involving the p-sublaplacian operator Δp,G on a Carnot group G, 1<p<Q. As a remarkable consequence, we obtain the exact rate of decay of the extremal functions for the subelliptic Sobolev inequality involving the Lp-norm of the horizontal gradient.