Carleman estimates and inverse problems for Dirac operators

2007/09/14 by Mikko Salo, Salo, Mikko, Leo Tzou +1
Mathematics · Computer Science · Engineering · #Numerical methods in inverse problems #Advanced Mathematical Modeling in Engineering #Composite Material Mechanics

paper · pdf · doi:10.48550/arxiv.0709.2282

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.

Citations

• A Global Uniqueness Theorem for an Inverse Boundary Value Problem

Related

• Inverse problems with partial data for a Dirac system: a Carleman estimate approach
• Carleman estimate for the Schrödinger equation and application to magnetic inverse problems
• Semiclassical estimates for the magnetic Schrödinger operator on the line
• Carleman estimates for global uniqueness, stability and numerical\n methods for coefficient inverse problems
• Uniqueness in an inverse boundary problem for a magnetic Schrödinger operator with a bounded magnetic potential