Stable determination of the first order perturbation of the biharmonic operator from partial data

TL;DR

This paper proves that it is possible to stably determine first order perturbations of the biharmonic operator using limited boundary measurements, with stability estimates of logarithmic type.

Contribution

It establishes the first stability results for the inverse problem of the biharmonic operator with first order perturbations from partial boundary data.

Findings

Log-type stability estimates are derived for the perturbations.

Stable determination is possible from measurements on arbitrarily small boundary subsets.

Results extend inverse boundary value problem theory to higher-order operators.

Abstract

We consider an inverse boundary value problem for the biharmonic operator with the first order perturbation in a bounded domain of dimension three or higher. Assuming that the first and the zeroth order perturbations are known in a neighborhood of the boundary, we establish log-type stability estimates for these perturbations from a partial Dirichlet-to-Neumann map. Specifically, measurements are taken only on an arbitrarily small open subsets of the boundary.