Stable determination of a second order perturbation of the polyharmonic operator by boundary measurements

TL;DR

This paper proves that second order perturbations of the polyharmonic operator can be uniquely identified from boundary measurements, providing a stability estimate in dimensions three and higher.

Contribution

It establishes the unique determination and stability estimate for second order perturbations of the polyharmonic operator using boundary data, advancing inverse boundary value problem theory.

Findings

Unique determination of second order perturbations from boundary measurements

Logarithmic stability estimate in dimensions n ≥ 3

Extension of inverse problem results to polyharmonic operators

Abstract

In this paper, we consider the inverse boundary value problem for the polyharmonic operator. We prove that the second order perturbations are uniquely determined by the corresponding Dirichlet to Neumann map. More precisely, we show in dimension $n \geq 3$, a logarithmic type stability estimate for the inverse problem under consideration.