Stability estimates in a partial data inverse boundary value problem for biharmonic operators at high frequencies

TL;DR

This paper investigates stability estimates for an inverse boundary value problem involving a biharmonic operator at high frequencies, providing explicit frequency dependence and improving previous stability results under mild regularity conditions.

Contribution

It establishes high-frequency stability estimates for the inverse problem, sharpening prior results by explicitly incorporating frequency dependence and relaxing regularity assumptions.

Findings

Derived explicit stability estimates depending on frequency

Improved stability results over previous work

Applicable under mild regularity assumptions

Abstract

We study the inverse boundary value problems of determining a potential in the Helmholtz type equation for the perturbed biharmonic operator from the knowledge of the partial Cauchy data set. Our geometric setting is that of a domain whose inaccessible portion of the boundary is contained in a hyperplane, and we are given the Cauchy data set on the complement. The uniqueness and logarithmic stability for this problem were established in [37] and [7], respectively. We establish stability estimates in the high frequency regime, with an explicit dependence on the frequency parameter, under mild regularity assumptions on the potentials, sharpening those of [7].