Abstract
The two layers inverse gravimetric problem is to determine the shape of the two layers in a body B, generating a given gravitational potential in the exterior of B. If the constant density of the two layers is given, the problem is reduced to the determination of the geometry of the interface between the two. The problem is known to be ill posed and therefore it needs a regularization, that for instance could have the form of the optimization of a Tikhonov functional. In this paper it is discussed why neither L 2 nor H 1, 2 are acceptable choices, the former giving too rough solutions, the latter too smooth. The intermediate Banach space of functions of Bounded Variation is proposed as a good solution space to allow for discontinuities, but not too wild oscillations of the interface. The problem is analyzed by standard variational techniques and existence of the optimal solution is proved.
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Capponi, M., Sampietro, D., Sansò, F. (2019). Regularized Solutions of the Two Layers Inverse Gravimetric Problem in the Space of Bounded Variation Functions. In: Novák, P., Crespi, M., Sneeuw, N., Sansò, F. (eds) IX Hotine-Marussi Symposium on Mathematical Geodesy. International Association of Geodesy Symposia, vol 151. Springer, Cham. https://doi.org/10.1007/1345_2019_77
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DOI: https://doi.org/10.1007/1345_2019_77
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