Carleman estimates for a subelliptic operator and unique continuation (Q1323154)

We establish a Carleman type inequality for the subelliptic operator \({\mathcal L}= \Delta_ z+ | z|^ 2 \partial_ t^ 2\) in \(\mathbb{R}^{n+1}\), \(n\geq 2\), where \(z\in \mathbb{R}^ n\), \(t\in \mathbb{R}\). As a consequence, we show that \(-{\mathcal L}+V\) has the strong unique continuation property at points of the degeneracy manifold \(\{(0,t)\in \mathbb{R}^{n+1}\mid t\in\mathbb{R}\}\) if the potential \(V\) is locally in certain \(L^ p\) spaces.