Stability for the multi-dimensional Borg--Levinson theorem of the biharmonic operator

TL;DR

This paper establishes a conditional stability estimate for the inverse spectral problem of the biharmonic operator, extending previous results from second to fourth order operators using resolvent estimates and Weyl law.

Contribution

It provides the first stability result for the inverse spectral problem of the biharmonic operator, generalizing prior work on second order operators.

Findings

Proves a Hölder stability estimate for the inverse spectral problem.

Extends inverse spectral stability results from Schrödinger to biharmonic operators.

Utilizes resolvent estimates and Weyl law for the biharmonic operator.

Abstract

In this paper, we prove a conditional H\"older stability estimate for the inverse spectral problem of the biharmonic operator. The proof employs the resolvent estimate and a Weyl-type law for the biharmonic operator which were obtained by the authors in \cite{LYZ}. This work extends nontrivially the result in \cite{stefanov} from the second order Schr\"{o}dinger operator to the fourth order biharmonic operator.