Volume 25, pp. 41-53, 2006.

Inverse source problem in a 3D ball from best meromorphic approximation on 2D slices

L. Baratchart, J. Leblond, and J.-P. Marmorat


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 [L. Baratchart et al., Recovery of pointwise sources or small inclusions in 2D domains and rational approximation, Inverse Problems, 21 (2005), pp. 51–74] an approach to these 2D inverse problem which is based on meromorphic approximation, and we present numerical results.

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Key words

inverse source problems, potential theory, meromorphic approximation

AMS subject classifications

31A25, 30E10, 30E25, 35J05

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