Inverse boundary value problems for polyharmonic operators with non-smooth coefficients

Abstract

We consider inverse boundary value problems for polyharmonic operators and in particular, the problem of recovering the coefficients of terms up to order one. The main interest of our result is that it further relaxes the regularity required to establish uniqueness. The proof relies on an averaging technique introduced by Haberman and Tataru for the study of an inverse boundary value problem for a second order operator.

26 pages Revised version adds a proof of Lemma 3.6 and minor corrections elsewhere Revised version in March 2025 adds a second file which provides a correction to the main result of the original paper

References in corpus (8)

• Uniqueness in Calderon's problem with Lipschitz conductivities
• Global uniqueness for the Calderón problem with Lipschitz conductivities
• Uniqueness in Calderón's problem for conductivities with unbounded gradient
• Stability estimates for the inverse boundary value problem for the biharmonic operator with bounded potentials
• Inverse problems for the perturbed polyharmonic operator with coefficients in Sobolev spaces with non-positive order
• The Bilinear Strategy for Calderón's Problem
• Recovery of the Derivative of the Conductivity at the Boundary
• Reconstructing a potential perturbation of the biharmonic operator on transversally anisotropic manifolds

Cited by in corpus (2)

• Stability estimates for an inverse boundary value problem for biharmonic operators with first order perturbation from partial data
• Stable determination of the first order perturbation of the biharmonic operator from partial data