Geodesic
Inverse source problem in a 3D ball from best meromorphic approximation on 2D slices
Electronic transactions on numerical analysis, Tome 25 (2006), pp. 41-53.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We show that the inverse monopolar or dipolar source problem in a 3D ball from overdetermined Dirichlet-Neumann data on the boundary sphere reduces to a family of 2D inverse branchpoint problems in cross sections of the sphere, at least when there are finitely many sources. We adapt from [7] an approach to these 2D inverse problem which is based on meromorphic approximation, and we present numerical results.
Classification : 31A25, 30E10, 30E25, 35J05
Keywords: inverse source problems, potential theory, meromorphic approximation 
@article{ETNA_2006__25__a29,
     author = {Baratchart, L. and Leblond, J. and Marmorat, J.-P.},
     title = {Inverse source problem in a {3D} ball from best meromorphic approximation on {2D} slices},
     journal = {Electronic transactions on numerical analysis},
     pages = {41--53},
     publisher = {mathdoc},
     volume = {25},
     year = {2006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2006__25__a29/}
}
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Baratchart, L.; Leblond, J.; Marmorat, J.-P. Inverse source problem in a 3D ball from best meromorphic approximation on 2D slices. Electronic transactions on numerical analysis, Tome 25 (2006), pp. 41-53. http://geodesic.mathdoc.fr/item/ETNA_2006__25__a29/