Carleman estimates for Baouendi-Grushin operators with applications to quantitative uniqueness and strong unique continuation

In this paper we establish some new $L^2-L^2$ Carleman estimates for the Baouendi-Grushin operators ${\mathcal{B}}_{\gamma }$, in (1.1) below. We apply such estimates to obtain: (i) an extension of the Bourgain-Kenig quantitative unique continuation; (ii) the strong unique continuation property for some degenerate sublinear equations.