LAUSR

We consider the following perturbed polyharmonic operator $$\mathcal {L}(x,D)$$L(x,D) of order 2m defined in a bounded domain $$\Omega \subset \mathbb {R}^n, n\ge 3$$Ω⊂Rn,n≥3 with smooth boundary, as $$ \mathcal {L}(x,D) \equiv (-\Delta )^m + \sum _{j,k=1}^{n}A_{jk} D_{j}D_{k} + \sum _{j=1}^{n}B_{j} D_{j} + q(x),$$L(x,D)≡(-Δ)m+∑j,k=1nAjkDjDk+∑j=1nBjDj+q(x), where A is a symmetric 2-tensor field, B and q are vector field and scalar potential respectively. We show that the coefficients $$A=[A_{jk}]$$A=[Ajk], $$B=(B_j)$$B=(Bj) and q can be recovered from the associated Dirichlet-to-Neumann data on the boundary. Note that this result shows an example of determining higher order (2nd order) symmetric tensor field in the class of inverse boundary value problem.