Unique determination of anisotropic perturbations of a polyharmonic operator from partial boundary data

Abstract: We study an inverse problem involving the unique recovery of several 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 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 Calder\'on-type inverse problems. We construct suitable complex geometric optics (CGO) solutions for the polyharmonic operators that reduces the inverse problem to uniqueness results for a generalized MRT. 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.