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Magnetic moment estimation and bounded extremal problems. (English) Zbl 1410.35025

Summary: We consider the inverse problem in magnetostatics for recovering the moment of a planar magnetization from measurements of the normal component of the magnetic field at a distance from the support. Such issues arise in studies of magnetic material in general and in paleomagnetism in particular. Assuming the magnetization is a measure with \(L^2\)-density, we construct linear forms to be applied on the data in order to estimate the moment. These forms are obtained as solutions to certain extremal problems in Sobolev classes of functions, and their computation reduces to solving an elliptic differential-integral equation, for which synthetic numerical experiments are presented.

MSC:

35J15 Second-order elliptic equations
35R30 Inverse problems for PDEs
35A35 Theoretical approximation in context of PDEs
42B37 Harmonic analysis and PDEs
86A22 Inverse problems in geophysics
45K05 Integro-partial differential equations
46F12 Integral transforms in distribution spaces
47N20 Applications of operator theory to differential and integral equations
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