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Boundary determination of electromagnetic and Lamé parameters with corrupted data. (English) Zbl 1472.35449

Summary: We study boundary determination for an inverse problem associated to the time-harmonic Maxwell equations and another associated to the isotropic elasticity system. We identify the electromagnetic parameters and the Lamé moduli for these two systems from the corresponding boundary measurements. In a first step we reconstruct Lipschitz magnetic permeability, electric permittivity and conductivity on the surface from the ideal boundary measurements. Then, we study inverse problems for Maxwell equations and the isotropic elasticity system assuming that the data contains measurement errors. For both systems, we provide explicit formulas to reconstruct the parameters on the boundary as well as its rate of convergence formula.

MSC:

35R30 Inverse problems for PDEs
35A02 Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness
35Q61 Maxwell equations
74B05 Classical linear elasticity
78A46 Inverse problems (including inverse scattering) in optics and electromagnetic theory
86A22 Inverse problems in geophysics
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