MOMENTUM RAY TRANSFORMS AND A PARTIAL DATA INVERSE PROBLEM FOR A POLYHARMONIC OPERATOR

We study an inverse problem involving the unique recovery of lower order anisotropic tensor perturbations of a polyharmonic operator in a bounded domain from the knowledge of the Dirichlet to Neumann map on a part of a boundary. The uniqueness proof relies on the inversion of generalized momentum ray transforms (MRT) for symmetric tensor fields, which we introduce for the first time to study Calderon-type inverse problems. The uniqueness result and the inversion formula we prove for generalized MRT could be of independent interest and we expect it to be applicable to other inverse problems for higher order operators involving tensor perturbations.