Inverse boundary problems for polyharmonic operators with unbounded potentials

We show that the knowledge of the Dirichlet–to–Neumann map on the boundary of a bounded open set in R^n for the perturbed polyharmonic operator (-Δ)^m +q with q∈ Ln/2m , n>2m , determines the potential q in the set uniquely. In the course of the proof, we construct a special Green function for the polyharmonic operator and establish its mapping properties in suitable weighted L^2 and L^p spaces. The L^p estimates for the special Green function are derived from L^p Carleman estimates with linear weights for the polyharmonic operator.