Fang Zhang

Carleman Estimates for Critical Electromagnetic Schr\"odinger Operators on Conic Manifolds

We establish an $L^p$--$L^q$-type Carleman estimate for the Schr\"odinger operator $H_{A,V}$ with scaling-critical electromagnetic singular potentials on a conical singular space $(X,g)$ of dimension $d\geq3$, where the metric is $g=dr^2+r^2h$ and $X=C(Y)=(0,\infty)_r\times Y$ is a product cone over the closed Riemanni...