Determining rough first order perturbations of the polyharmonic operator

We show that the knowledge of Dirichlet to Neumann map for rough $A$ and $q$ in $(-\mathrm{\Delta }{)}^m+A\cdot D+q$ for $m\ge 2$ for a bounded domain in ${\mathbb{R}}^n$, $n\ge 3$ determines $A$ and $q$ uniquely. This unique identifiability is proved via construction of complex geometrical optics solutions with sufficient decay of remainder terms, by using property of products of functions in Sobolev spaces.