The Calderón problem for conormal potentials, I: Global uniqueness and reconstruction
Allan Greenleaf, Matti Lassas, and Gunther Uhlmann
We consider inverse problems for Schrödinger 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 Schrödinger equation in generalized sense (as solution of minimization problem), we give certain counter examples to uniqueness of inverse problem.