Stability estimates for the inverse boundary value problem for the biharmonic operator with bounded potentials

TL;DR

This paper establishes stability estimates for inverse boundary value problems involving the biharmonic operator with bounded potentials, providing logarithmic and double logarithmic stability results depending on the measurement boundary extent.

Contribution

It introduces new stability estimates for the inverse problem of the biharmonic operator with bounded potentials, extending results to partial boundary measurements.

Findings

Logarithmic stability estimates for full boundary measurements.

Double logarithmic stability estimates for measurements on slightly more than half the boundary.

Quantitative bounds for the inverse problem stability.

Abstract

In this article, stability estimates are given for the determination of the zeroth-order bounded perturbations of the biharmonic operator when the boundary Neumann measurements are made on the whole boundary and on slightly more than half the boundary, respectively. For the case of measurements on the whole boundary, the stability estimates are of ln-type and for the case of measurements on slightly more than half of the boundary, we derive estimates that are of ln ln-type.