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In this paper we present some aspects of an inverse source problem in an elliptic equation with varying coefficients, using partial Dirichlet boundary measurements. A uniqueness result is established for dipolar sources including their number. Additionally, assuming the number of dipoles known, a stability result is obtained and an efficient numerical identification method is developed. Finally, numerical experiments illustrate the effectiveness of the approach and a discussion is given on electroencephalography (EEG) in neonates.

An inverse dipole source problem in inhomogeneous media: Application to the EEG source localization in neonates