Determination of Lower Order Perturbations of a Polyharmonic Operator in Two Dimensions

We study an inverse boundary value problem for a polyharmonic operator in two dimensions. We show that the Cauchy data uniquely determine all the anisotropic perturbations of orders at most $m-1$ and several perturbations of orders $m$ to $2m-2$ under some restriction. The uniqueness proof relies on the $\bar{\mathrm{\partial }}$-techniques and the method of stationary phase.