Inverse problems with partial data for a Dirac system: a Carleman estimate approach

TL;DR

This paper establishes the unique determination of material parameters in a Dirac system with magnetic and electric potentials from boundary measurements on possibly small boundary subsets, using advanced Carleman estimates.

Contribution

It introduces a novel approach combining Carleman estimates and a reduction technique to handle partial boundary data in Dirac systems.

Findings

Proves uniqueness of material parameters from partial boundary data.

Develops Carleman estimates for singular coefficients in Dirac systems.

Reduces boundary measurement problem to a second order system.

Abstract

We prove that the material parameters in a Dirac system with magnetic and electric potentials are uniquely determined by measurements made on a possibly small subset of the boundary. The proof is based on a combination of Carleman estimates for first and second order systems, and involves a reduction of the boundary measurements to the second order case. For this reduction a certain amount of decoupling is required. To effectively make use of the decoupling, the Carleman estimates are established for coefficients which may become singular in the asymptotic limit.