On the existence of Parker’s ideal bodies
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Ballani, L., Stromeyer, D.: The inverse gravimetric problems: a Hilbert Space approach. In: Proceedings of International Symposium in Figure of the Earth, the Moon and the Other Planets, pp. 359–373 (1983)
Barzaghi, R., Sansò, F.: Remarks on the inverse gravimetric problem. Geophys. J. Astrom. Soc. 92, 505–511 (1986)
Falconer, K.J.: The Geometry of Fractal Sets. Cambridge Tracts in Mathematics, vol. 85. Cambridge University Press, Cambridge (1985)
Freeden, W., Nashed, M.Z.: Inverse gravimetry: background material and multiscale mollifier approaches. GEM Int. J. Geomath. 9, 199–264 (2018a)
Freeden, W., Nashed, M.Z.: Ill-posed problems: operator methodologies of resolution and regularization. In: Freeden, W., Nashed, M.Z. (eds.) Handbook of Mathematical Geodesy: Functional Analytic and Potential Methods, pp. 201–314. Springer, New York (2018b)
Freeden, W., Sansò, F.: Geodesy and mathematics: interactions, acquisitions and open problems. In: Proceedings of IX Hotine-Marussi Symposium on Mathematical Geodesy, IAG Symposium, vol. 151, pp. 219–250 (2020)
Isakov, V.: Inverse Source Problems. Mathematical Surveys and Monographs Series, vol. 34. Am. Math. Society, Providence RI (1990)
Jerison, D.S., Kenig, C.E.: Boundary value problems on Lipschitz domains. In: Littman, W. (ed) Studies in Partial Differential Equations, vol. 23, pp. 1–67 (1982)
Lucchetti, R., Sansò, F.: A class of sets where convergence in Hausdorff sense and in measure coincide. Atti Accademia Peloritana dei Pericolanti (Scienze Fisiche Matematiche e Naturali (2020) (in print)
McLean, W.: Strongly Elliptic Systems and Boundary Integral Equations. Cambridge University Press, Cambridge (2000)
Michel, V., Fokas, A.S.: A unified approach to various techniques for the non-uniqueness of the inverse gravimetric problem and wavelet-based methods. Inverse Problems 24, 045019 (2008)
Novikov, P.S.: Sur le problème inverse du potentiel. Dokl. Akad. Nauk SSSR 18, 165–168 (1938)
Parker, R.L.: Theory of ideal bodies for gravity interpretation. Geophys. J. R. Astrom. Soc. 42, 315–334 (1975)
Sampietro, D., Sansò, F.: Uniqueness theorems of inverse gravimetric problems. In: Proceedings of VII Hotine-Marussi Symposium on Mathematical Geodesystem, IAG Symposium, vol. 137, pp. 111–115 (2012)
Sansò, F.: Internal collocation. Mem. Acc. Naz. dei Lincei 16(1), 5–52 (1980)
Sansò, F.: The forward modelling of the gravity field. In: Sansò, F., Sideris, M.G. (eds.) Geoid Determination: Theory and Methods, pp. 3–71. Springer, Berlin (2013)
Sansò, F.: On the regular decomposition of the inverse gravimetric problems in non-$$L^2$$ spaces. Int. J. Geomath. 5(1), 33–61 (2014)
Yosida, K.: Functional Analysis. Springer, Berlin (1980)