Determining rough first order perturbations of the polyharmonic operator

Abstract

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

arXiv admin note: text overlap with arXiv:1510.02160