Increasing stability for the conductivity and attenuation coefficients

TL;DR

This paper demonstrates that the stability of recovering conductivity and attenuation coefficients from boundary data improves as the frequency increases, using complex geometrical optics solutions.

Contribution

It introduces bounds indicating increasing stability in inverse boundary value problems for Maxwell and Schrödinger equations at higher frequencies.

Findings

Stability improves with increasing frequency.

Derived bounds support increasing stability.

Applicable to Maxwell and Schrödinger inverse problems.

Abstract

In this work we consider stability of recovery of the conductivity and attenuation coefficients of the stationary Maxwell and Schr\"odinger equations from a complete set of (Cauchy) boundary data. By using complex geometrical optics solutions we derive some bounds which can be viewed as an evidence of increasing stability in these inverse problems when frequency is growing.