We consider an inverse boundary value problem for an operator whose principal part is the polyharmonic operator. We show that the coefficients of lower order terms of degree up to order one are uniquely determined by information about solutions at the boundary. The main interest of our result is that it further relaxes the regularity required to establish uniqueness. The proof relies on an averaging technique introduced by Haberman and Tataru for the study of an inverse boundary value problem for a second order operator. The results discussed are joint work with Landon Gauthier.

We consider the determination of a potential perturbation of the Schrödinger equation from the map taking the initial data at time 0 to the values of the solution at time T. We prove the uniqueness of this inverse problem. This is a joint work with Pedro Caro.