@ARTICLE{BCHLLM2019,
  author = 	 {Baratchart, Laurent and Chevillard, Sylvain and Hardin, Douglas P. and Leblond, Juliette and Lima, Eduardo Andrade and Marmorat, Jean-Paul},
  title = 	 {{Magnetic moment estimation and bounded extremal problems}},
  journal = 	 {{Inverse Problems and Imaging}},
  year = 	 {2019},
  volume = 	 {13},
  number = 	 {1},
  pages = 	 {39--67},
  month = 	 {Feb},
  hal = {hal-01623991},
  doi = {10.3934/ipi.2019003},
  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. },
  keywords = {elliptic partial differential equations, best constrained approximation in Hilbert spaces, harmonic functions, paleomagnetism, Inverse moment estimation problems, geosciences and planetary sciences}
}