Carleman estimates and inverse problems for Dirac operators

TL;DR

This paper establishes Carleman estimates for Dirac operators using limiting weights, and applies these results to inverse boundary value problems for recovering magnetic fields and potentials.

Contribution

It extends the concept of limiting Carleman weights from Laplacian to Dirac operators and applies this to inverse problems involving the Pauli Dirac operator.

Findings

Limiting Carleman weights for Laplacian also apply to Dirac operators.

Derived new Carleman estimates for Dirac operators.

Successfully recovered magnetic fields and electric potentials from boundary data.

Abstract

We consider limiting Carleman weights for Dirac operators and prove corresponding Carleman estimates. In particular, we show that limiting Carleman weights for the Laplacian also serve as limiting weights for Dirac operators. As an application we consider the inverse problem of recovering a Lipschitz continuous magnetic field and electric potential from boundary measurements for the Pauli Dirac operator.