Inverse problems for polyharmonic operators with lower order perturbations (Joint with IP seminar)  

 Abstract:  We consider an inverse problem of recovering lower order perturbations of a polyharmonic operator on a bounded domain $\Omega$ of dimension 3 or higher, from the Dirichlet to Neumann map defined on the boundary. We consider the operator
$$\mathcal{L}=(-\mathrm{\Delta }{)}^m+\sum _{j,k=1}^n{A}_{jk}(x){\partial }_{x_j}{\partial }_{x_k}+\sum _{j=1}^n{B}_j(x){\partial }_{x_j}+q(x),m\ge 2,$$
where $A:= (A_{jk})$ is a symmetric matrix, $B:=\{B_1,\dots,B_n\}$ is a vector field and $q$ is a bounded function on the domain $\Omega$. We discuss the case of $m>2$, where we can recover the perturbations $A$, $B$ and $q$ in $\Omega$ from the Dirichlet to Neumann map defined on the boundary $\partial \Omega$; as well as the case of $m=2$, where there is an obstruction in the unique recovery of the perturbations from the boundary data.