Determining a first order perturbation of the biharmonic operator by partial boundary measurements

We consider an operator Δ2+A(x)⋅D+q(x) with the Navier boundary conditions on a bounded domain in Rn, n⩾3. We show that a first order perturbation A(x)⋅D+q can be determined uniquely by measuring the Dirichlet-to-Neumann map on possibly very small subsets of the boundary of the domain. Notice that the corresponding result does not hold in general for a first order perturbation of the Laplacian.