Inverse problems for the perturbed polyharmonic operator with coefficients in Sobolev spaces with non-positive order

Abstract

We show that the knowledge of the Dirichlet-to-Neumann map on the boundary of a bounded open set in ${\mathbb{R}}^n$, $n\ge 3$, for the perturbed polyharmonic operator $(-\Delta {)}^m+A\cdot D+q$, $m\ge 2$, with $n>m$, $A\in W^{-\frac{m-2}{2},\frac{2n}{m}}$ and $q\in W^{-\frac{m}{2}+\delta ,\frac{2n}{m}}$, with $0<\delta <1/2$, determines the potentials $A$ and $q$ in the set uniquely. The proof is based on a Carleman estimate with linear weights and with a gain of two derivatives and on the property of products of functions in Sobolev spaces.

24 pages, statement of main result was incorrect in the earlier version and has been corrected and modified

References in corpus (2)

• Global uniqueness for the Calderón problem with Lipschitz conductivities
• Uniqueness in Calderón's problem for conductivities with unbounded gradient

Cited by in corpus (4)

• Inverse boundary value problems for polyharmonic operators with non-smooth coefficients
• Stability estimates for an inverse boundary value problem for biharmonic operators with first order perturbation from partial data
• The obstacle scattering for the biharmonic equation
• Stable determination of the first order perturbation of the biharmonic operator from partial data