Inverse problems with partial data for a Dirac system: a Carleman estimate approach. (English) Zbl 1197.35329
Summary: 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.
MSC:
| 35R30 | Inverse problems for PDEs |
| 35Q60 | PDEs in connection with optics and electromagnetic theory |
| 78A46 | Inverse problems (including inverse scattering) in optics and electromagnetic theory |
| 35B45 | A priori estimates in context of PDEs |
| 78A05 | Geometric optics |
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