Boundary determination of electromagnetic and Lam\'e parameters with corrupted data

TL;DR

This paper addresses the boundary determination of electromagnetic and elastic parameters from boundary measurements, providing explicit reconstruction formulas and analyzing the effects of measurement errors.

Contribution

It introduces explicit formulas for boundary parameter reconstruction in Maxwell and elasticity systems, including error analysis under corrupted data.

Findings

Reconstructed boundary electromagnetic parameters and Lamé moduli from ideal measurements.

Derived explicit formulas for boundary reconstruction in both systems.

Analyzed convergence rates of the reconstruction formulas with measurement errors.

Abstract

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 Lam\'e 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.