Stability of inverse boundary value problem for the fourth-order Schr\"{o}dinger equation

TL;DR

This paper investigates the stability of reconstructing potentials in a fourth-order Schrödinger equation from boundary data, using complex geometric optics and Fourier analysis, with results depending on prior information about the potential.

Contribution

It provides new stability estimates for the inverse boundary value problem for the fourth-order Schrödinger equation, extending previous results to perturbed potentials with specific regularity and support conditions.

Findings

Established stability estimates depending on a priori information.

Utilized complex geometric optics solutions and Fourier analysis techniques.

Results applicable to perturbed potentials with regularity and support constraints.

Abstract

This paper is concerned with the stability of the inverse boundary value problem for the perturbed fourth-order Schr\"{o}dinger equation in a bounded domain with Cauchy data. We establish stability results for the perturbed potential relying on boundary measurements. The estimates depend on various a priori information regarding the regularity and the support of the inhomogeneity. The proof primarily utilizes the complex geometric optics solution method and Fourier analysis.