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- Title
Magnetic moment estimation and bounded extremal problems.
- Authors
Baratchart, Laurent; Chevillard, Sylvain; Hardin, Douglas; Leblond, Juliette; Lima, Eduardo Andrade; Marmorat, Jean-Paul
- 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 L2-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.
- Subjects
MAGNETIC moments; EXTREMAL problems (Mathematics); MAGNETOSTATICS; ELLIPTIC differential equations; HILBERT space
- Publication
Inverse Problems & Imaging, 2019, Vol 13, Issue 1, p39
- ISSN
1930-8337
- Publication type
Article
- DOI
10.3934/ipi.2019003