Inverse problems for the perturbed polyharmonic operator with coefficients in Sobolev spaces with non-positive order

We show that the knowledge of the Dirichlet-to-Neumann map on the boundary of a bounded open set in R n , n ≥ 3 , for the perturbed polyharmonic operator ( − Δ ) m + A · D + q , m ≥ 2 , with 2 n > m , A ∈ W − m − 2 2 , 2 n m and q ∈ W − m 2 , 2 n m , determines the potentials A and q in the set uniquely. The proof is based on a Carleman estimate with linear weights and with a gain of two derivatives and on the property of products of functions in Sobolev spaces.