| Contents |
| We will show that if the potential of a Schr\"odinger equation is in $L^p$, $p>2$, then the boundary data consisting of traces and normal derivatives of all $H^1$-solutions determines the potential. If it is in a Sobolev space with a positive smoothness parameter, then there is conditional stability. This is made possible by proving a Carleman estimate with stronger decay rate than before. This fills a gap from Bukhgeim's paper of 2008. The result is based on a joint work with Imanuvilov and Yamamoto. |
|