Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Local existence of the solution to a nonlinear inverse problem in gravitation


Author: M. C. Jorge
Journal: Quart. Appl. Math. 45 (1987), 287-292
MSC: Primary 86A20; Secondary 31B20, 35R30
DOI: https://doi.org/10.1090/qam/895098
MathSciNet review: 895098
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Abstract: We consider the problem of modeling the external gravitational field of the earth from measurements of its intensity on the surface. The problem is formulated as a nonlinear oblique boundary value problem for the external gravitational potential. The equation for the potential is approximated for small anomalies and solved by a regular perturbation expansion. The convergence of the series is proved using Schauder estimates, and local existence for small anomalies is established. The technique used to prove the convergence of the series is in the same spirit as the Cauchy--Kowalewsky estimates. This study completes previous work done by Backus who proved uniqueness of the solution.


References [Enhancements On Off] (What's this?)

  • [1] George E. Backus, Application of a non-linear boundary-value problem for Laplace’s equation to gravity and geomagnetic intensity surveys, Quart. J. Mech. Appl. Math. 21 (1968), 195–221. MR 0227444, https://doi.org/10.1093/qjmam/21.2.195
  • [2] G. E. Backus, Non-uniqueness of the external geomagnetic field determined by surface intensity measurements, J. Geophys. Res. 75, 6339-6341 (1970)
  • [3] R. Courant and D. Hilbert, Methods of mathematical physics, Vol. 2., Interscience, New York. 49, 1962
  • [4] N. M. Günter, Potential theory, Dover, New York, 1967
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  • [6] V. D. Kupradze, Three dimensional problems of the mathematical theory of elasticity and thermoelasticity, North-Holland Publishing Company, Amsterdam, 1976

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DOI: https://doi.org/10.1090/qam/895098
Article copyright: © Copyright 1987 American Mathematical Society


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