Inverse boundary value problems for the perturbed polyharmonic operator

Abstract

We show that a first order perturbation A ( x ) ⋅ D + q ( x ) A(x)\cdot D+q(x) of the polyharmonic operator ( − Δ ) m (-\Delta )^m , m ≥ 2 m\ge 2 , can be determined uniquely from the set of the Cauchy data for the perturbed polyharmonic operator on a bounded domain in R n \mathbb {R}^n , n ≥ 3 n\ge 3 . Notice that the corresponding result does not hold in general when m = 1 m=1 .