We show that the knowledge of the Dirichlet–to–Neumann map on the boundary of a bounded open set in for the perturbed polyharmonic operator with , , determines the potential 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 and spaces. The estimates for the special Green function are derived from Carleman estimates with linear weights for the polyharmonic operator.
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Katsiaryna Krupchyk, Gunther Uhlmann, Inverse boundary problems for polyharmonic operators with unbounded potentials. J. Spectr. Theory 6 (2016), no. 1, pp. 145–183DOI 10.4171/JST/122