linearized inverse problem for biharmonic operators at high frequencies

TL;DR

This paper investigates the increasing stability in inverse boundary value problems for biharmonic operators at high frequencies, revealing enhanced stability and exponential effects of attenuation in linearized models.

Contribution

It introduces a linearized approach to analyze increasing stability for biharmonic inverse problems at high frequencies, including effects of attenuation.

Findings

Stability improves as frequency increases

Exponential dependence of attenuation on stability estimates

Linearized model effectively captures stability phenomena

Abstract

In this paper, we study the phenomenon of increasing stability in the inverse boundary value problems for the biharmonic equation. By considering a linearized form, we obtain an increasing Lipschitz-like stability when k is large. Furthermore, we extend the discussion to the linearized inverse biharmonic potential problem with attenuation, where an exponential dependence of the attenuation constant is traced in the stability estimate.