# Determining rough first order perturbations of the polyharmonic operator

## TL;DR

This paper proves the unique determination of rough coefficients in a polyharmonic operator from boundary measurements, extending inverse problem results to operators with less regular coefficients.

## Contribution

It introduces a method to establish uniqueness for inverse boundary value problems involving polyharmonic operators with rough coefficients using complex geometrical optics solutions.

## Key findings

- Unique identifiability of coefficients A and q
- Construction of complex geometrical optics solutions with decay
- Application of Sobolev space product properties

## Abstract

We show that the knowledge of Dirichlet to Neumann map for rough $A$ and $q$ in $(-\Delta)^m +A\cdot D +q$ for $m \geq 2$ for a bounded domain in $\mathbb{R}^n$, $n \geq 3$ 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.