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The boundary problems of physical geodesy

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References

  1. Agmon, S., A. Douglis and L. Nirenberg. Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions, I. Comm. Pure Appl. Math. 12, 623–727(1959).

    Google Scholar 

  2. Gromov, M. L. Smoothing and inversion of differential operators. Mat. Sbornik 88 (130), 382–441 (1972) (Russian). Also in Math. USSR Sbornik 17, 381–434 (1972).

    Google Scholar 

  3. Gromov, M. L. and V. A. Rokhlin. Embeddings and immersions in Riemannian geometry. Usp. Mat. Nauk 25 (5) (155), 3–62 (1970) (Russian). Also in Russian Math. Surveys 25, (5) 1–57 (1970).

    Google Scholar 

  4. Heiskanen, W. A. and H. Moritz. Physical geodesy. San Francisco and London: W. H. Freeman and Co. 1967.

    Google Scholar 

  5. Hörmander, L. Linear partial differential operators. Berlin-Göttingen-Heidelberg: Springer 1963.

    Google Scholar 

  6. Jacobowitz, H. Implicit function theorems and isometric embeddings. Ann. of Math. 95, 191–225 (1972).

    Google Scholar 

  7. Kato, T. Perturbation theory for linear operators. Berlin-Göttingen-Heidelberg: Springer 1966.

    Google Scholar 

  8. Krarup, T. Letters on Molodensky's problem, III. Unpublished manuscript.

  9. Moritz, H. Convergence of Molodensky's series. Report 183, Department of Geodetic Science, Ohio State University 1972.

  10. Moser, J. A new technique for the construction of solutions of non-linear differential equations. Proc. Nat. Acad. Sci. USA 47, 1824–1831 (1961).

    Google Scholar 

  11. Moser, J. A rapidly convergent iteration method and nonlinear differential equations. Ann. Scuola Norm. Sup. Pisa (3) 20, 265–315, 499–535 (1966).

    Google Scholar 

  12. Moser, J. On the construction of almost periodic solutions for ordinary differential equations. Proc. Int. Conf. Fund. Anal, and Related Topics, 60–67. Tokyo 1969.

  13. Nash, J. The imbedding problem for Riemannian manifolds. Ann. of Math. 63, 20–63 (1956).

    Google Scholar 

  14. Schwartz, J. T. On Nash's implicit functional theorem. Comm. Pure Appl. Math. 13, 509–530 (1960).

    Google Scholar 

  15. Schwartz, J. T. Nonlinear functional analysis. New York, London, Paris: Gordon and Breach, 1969.

    Google Scholar 

  16. Stein, E. M. and G. Weiss. Interpolation of operators with change of measures. Trans. Amer. Math. Soc. 87, 159–172 (1958).

    Google Scholar 

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Communicated by J. Serrin

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Hörmander, L. The boundary problems of physical geodesy. Arch. Rational Mech. Anal. 62, 1–52 (1976). https://doi.org/10.1007/BF00251855

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