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Journal Articles Inverse Problems and Imaging Year : 2019

Magnetic moment estimation and bounded extremal problems

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Abstract

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.
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Dates and versions

hal-01623991 , version 1 (26-10-2017)
hal-01623991 , version 2 (10-12-2018)

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Laurent Baratchart, Sylvain Chevillard, Douglas P. Hardin, Juliette Leblond, Eduardo Andrade Lima, et al.. Magnetic moment estimation and bounded extremal problems. Inverse Problems and Imaging , 2019, 13 (1), pp.29. ⟨10.3934/ipi.2019003⟩. ⟨hal-01623991v2⟩
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