Abstract
In this paper a series solution for Zagrebin’s problem is proposed, based in a sequence of simple Molodensky’s type boundary value problems in the domain exterior to the ellipsoid of reference. A sufficient condition is stated for the convergence of this series in terms of the second eccentricity and constants some of them related to properties of the Hölder norms and a Schauder estimate for the simple problem of Molodensky in that domain.
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References
Bjerhammar, A. (1966) On the determination of the shape of the geoid and the shape of the earth from ellipsoidal surface of reference, Bull. Geod., 81, 235–264.
Dautray, R. and Lions, J-L. (1990) Mathematical analysis and numerical methods for science and technology, Vol. 1, Springer-Verlag, Berlin/ Heidelberg/New York.
Gilbarg, D. and Trudinger, N.S. (1983) Elliptic partial differential equations of second order, 2nd. Ed., Springer-Verlag, Berlin/ Heidelberg/ New York/ Tokyo.
Heck, B. (1991) On the linearized boundary value problems of physical geodesy, Dept. of Geod. Sci. Rep. 407, Ohio State Univ., Columbus.
Heiskanen, W. A. and Moritz, H. (1967) Physical Geodesy, W. H. Freeman and Co., San Francisco/Londres.
Holota, P. (1981) Direct methods for geodetic boundary problems, Proceedings 4th. Int. Symp. “Geodesy and Physics of the Earth”, Veroff. d. Zentr. Inst. f. Phys. d. Erde, Nr. 63, 2, Potsdam, 215–230.
Hörmander, L. (1976) The boundary problems of physical geodesy, Arch. Rational Mech. Anal., 62, 1–52.
Jorge, M.C. (1987) Local existence of the solution to a nonlinear inverse problem in gravitation, Quart. Appl. Math., 45 (2), 287–292.
Krarup, T. (1973) Letters on Molodensky’s problem, Unpublished manuscript.
Lieberman, G.M. (1986) Intermediate Schauder estimates for oblique derivative problems, Arch. Rational Mech. Anal., 93 (2), 129–134
Molodenskii, M. S., Eremeev, V. F. and Yurkina, M. I. (1962) Methods for study of the external gravitational field and figure of the earth, Transí. from Russian (1960), Israel Program for Scientific Translations, Jerusalem.
Otero, J. (1995) Unpublished manuscript, in preparation. (Tentative title: A uniqueness theorem for Zagreb in’s problem.)
Sacerdote, F. and Sansò, F. (1983) The current situation in the linear problem of Molodenskii, Atti. Accad. Naz. Lincei CI. Sci. Fis. Mat. Natur. Rend. Lincei (8) 75, 119–126.
Sacerdote, F. and Sansò, F. (1990) On the analysis of the fixed-boundary gravimetric boundary-value problem, Proceedings II Hotine-Marussi Symposium, Pisa, 507–516
Sansò, F. (1978) The local solvability of Molodensky’s problem in gravity space, Man. Geod., 3, 157–227.
Sansò, F. (1981a) Recent advances in the theory of the geodetic boundary value problem, Rev. Geophys. Space Phys., 19, 437–449.
Sansò, F. (1981b) The point on the simple Molodensky’s problem, Atti. Accad. Naz. Lincei CI. Sci. Fis. Mat. Natur. Rend. Lincei (8) 71, 87–94.
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© 1995 Springer-Verlag Berlin Heidelberg
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Otero, J., Capdevila, J. (1995). A Series Solution for Zagrebin’s Problem. In: Sansò, F. (eds) Geodetic Theory Today. International Association of Geodesy Symposia, vol 114. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-79824-5_36
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DOI: https://doi.org/10.1007/978-3-642-79824-5_36
Publisher Name: Springer, Berlin, Heidelberg
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