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

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].

References in corpus (1)

• Stability estimates for the inverse boundary value problem for the biharmonic operator with bounded potentials

Cited by in corpus (3)

• Stability estimates for an inverse boundary value problem for biharmonic operators with first order perturbation from partial data
• High frequency stability estimates for a partial data inverse problem
• Stable determination of the first order perturbation of the biharmonic operator from partial data