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Magnetic moment estimation and bounded extremal problems

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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Submitted on : Monday, December 10, 2018 - 2:19:12 PM
Last modification on : Wednesday, November 17, 2021 - 12:31:05 PM
Long-term archiving on: : Monday, March 11, 2019 - 2:33:06 PM


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  • HAL Id : hal-01623991, version 2


Laurent Baratchart, Sylvain Chevillard, Douglas Hardin, Juliette Leblond, Eduardo Lima, et al.. Magnetic moment estimation and bounded extremal problems. Inverse Problems and Imaging , AIMS American Institute of Mathematical Sciences, 2019, 13 (1), pp.29. ⟨hal-01623991v2⟩



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