Nondegeneracy of the bubble for the critical p-Laplace equation

Abstract We prove the non-degeneracy of the extremals of the Sobolev inequality \[ \int_{\mathbb R^N}|\nabla u|^p\,\rd x\ge \mathcal S_p\int_{\open R^N}|u|^\frac{Np}{N-p}\,\rd x,\quad u\in \mathcal D^{1,p}(\open R^N) \] when 1 < p < N , as solutions of a critical quasilinear equation involving the p -Laplacian.