Allan Greenleaf, Matti Lassas, and Gunther Uhlmann
We consider inverse problems for Schr\"odinger operator in the case of potential having co-normal singularities in dimensions $n\geq 3$. For instance, in the case where singularity is on hypersurface $H\subset \mathbb R^n$, we allow singularities of type $dist(x,H)^{-1+\alpha},$ $\alpha>0$. Moreover, by considering Schr\"odinger equation in generalized sense (as solution of minimization problem), we give certain counter examples to uniqueness of inverse problem.