Determining a first order perturbation of the biharmonic operator by   partial boundary measurements
  We consider an operator $\Delta^2 + A(x)\cdot D+q(x)$ with the Navier boundary conditions on a bounded domain in $R^n$, $n\ge 3$. We show that a first order perturbation $A(x)\cdot D+q$ 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. 
Katsiaryna Krupchyk, Matti Lassas, Gunther Uhlmann
math.AP math-ph math.MP