Inverse boundary problems for polyharmonic operators with unbounded potentials
Katsiaryna Krupchyk, Gunther A. Uhlmann · Journal of Spectral Theory · 2016
We show that the knowledge of the Dirichlet–to–Neumann map on the boundary of a bounded open set in \mathbb R^n for the perturbed polyharmonic operator (-\Delta)^m +q with q\in L^{\frac{n}{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.