THE CALDERÓN PROBLEM FOR CONORMAL POTENTIALS, I: GLOBAL UNIQUENESS AND RECONSTRUCTION

ALLAN GREENLEAF MATTI LASSAS GUNTHER UHLMANN

Abstract. We consider inverse problems for Schrödinger operator in the case of potential having co-normal singularities in dimensions n ≥ 3. For instance, in the case where singularity is on hypersurface H ⊂ ℝ^{n}, we allow singularities of type dist(x, H)^{−1+α}, α > 0. Moreover, by considering Schrödinger equation in generalized sense (as solution of minimization problem), we give certain counter examples to uniqueness of inverse problem.