Determining a first order perturbation of the biharmonic operator by partial boundary measurements (Q665498)

A uniqueness result for the inverse problem for the perturbed biharmonic operator \(L=\Delta^{2}+A(x) \cdot D + q(x)\) (\(A=(A_{j})_{1\leq j \leq n} \in C^{4}( \bar{\Omega}, \mathbb{C}^{n})\), \(n\geq 3\), \(q \in L^{\infty}(\Omega, \mathbb{C})\), \(\Omega\) a bounded simply connected domain with smooth connected boundary) with Navier boundary conditions \(u |_{\partial \Omega} = \Delta u |_{\partial \Omega} =0\) is proved. It is shown that if \(0\) is not an eigenvalue of \(L\), then the vector potential \(A\) and the scalar potential \(q\) are uniquely determined by measuring the Dirichlet-to-Neumann map on a possibly small subset of the boundary of \(\Omega\), depending on the shape of the boundary.