Recovering nonsmooth coefficients for higher-order perturbations of a polyharmonic operator

Abstract

We consider an inverse problem for a higher order elliptic operator where the principal part is the polyharmonic operator $(-\Delta {)}^m$ with $m\ge 2$. We show that the map from the coefficients to a certain bilinear form is injective. We have a particular focus on obtaining these results under lower regularity on the coefficients. It is known that knowledge of this bilinear form is equivalent to a knowledge of a Dirichlet to Neumann map or the Cauchy data for solutions.

42 pages, second version includes minor edits and corrections made during review of the paper