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
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},
     year = {2006},
     volume = {25},
     zbl = {1122.35149},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2006__25__a29/}
}
TY  - JOUR
AU  - Baratchart,  L.
AU  - Leblond,  J.
AU  - Marmorat,  J.-P.
TI  - Inverse source problem in a 3D ball from best meromorphic approximation on 2D slices
JO  - Electronic transactions on numerical analysis
PY  - 2006
SP  - 41
EP  - 53
VL  - 25
UR  - http://geodesic.mathdoc.fr/item/ETNA_2006__25__a29/
LA  - en
ID  - ETNA_2006__25__a29
ER  - 
%0 Journal Article
%A Baratchart,  L.
%A Leblond,  J.
%A Marmorat,  J.-P.
%T Inverse source problem in a 3D ball from best meromorphic approximation on 2D slices
%J Electronic transactions on numerical analysis
%D 2006
%P 41-53
%V 25
%U http://geodesic.mathdoc.fr/item/ETNA_2006__25__a29/
%G en
%F ETNA_2006__25__a29
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/