Bulletin Géodésique

, Volume 55, Issue 1, pp 17–30 | Cite as

The geodetic boundary value problem and the coordinate choice problem

  • Fernando Sansò
Article

Summary

The geodetic boundary value problem (g.b.v.p.) is a free boundary value problem for the Laplace operator: however, under suitable change of coordinates, it can be transformed into a fixed boundary one. Thus a general coordinate choice problem arises: two particular cases are more closely analyzed, namely the gravity space approach and the intrinsic coordinates (Marussi) approach.

Keywords

Field Equation Free Boundary Gravitational Field Gravity Field Spherical Approximation 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. [1]
    T. KRARUP: ╕etters on Molodensky’s Problem”—(manuscript).Google Scholar
  2. [2]
    A. MARUSSI: “Fondamenti di geodesia intrinseca”—Commiss. Geodet. Italiana, III serie, “Memorie”, n. 7, 1951.Google Scholar
  3. [3]
    A. MARUSSI: “Tensor Calculus”—in: Mathematical Geodesy. Methoden und Vertharen der mathematischen Physik, Band 13, 1975.Google Scholar
  4. [4]
    H. MORITZ: “Recent Developments in the Geodetic Boundary Value Problem”, Dept. of Geodetic Science, Rept. 266—Ohio State University, 1977.Google Scholar
  5. [5]
    H. MORITZ: “Advanced Physical Geodesy”—Karlsruhe: Wichmann, 1980.Google Scholar
  6. [6]
    F. SANSÓ: “The Geodetic Boundary Value Problem in Gravity Space”—Memorie Accad. Naz. Lincei, Roma, 1977.Google Scholar
  7. [7]
    F. SANSÓ: “Molodensky’s Problem in Gravity Space: a Review of First Results”—Bulletin Géodésique, 1978.Google Scholar
  8. [8]
    F. SANSÒ: “On the Local Solvability of Molodensky’s Problem in Gravity Space”—Manuscripta Geodaetica, 1979.Google Scholar
  9. [9]
    F. SANSÒ: “The Boundary Value Problems in the Representation of the Gravity Field”—XVII General Assembly of I.U.G.G., Canberra. (in print).Google Scholar
  10. [10]
    K.J. WITSCH: “Ein schiefes Randwertproblem zu einer elliptischen Differentialgleichung zweiter Ordnung mit einer explizitenL z-Abschätzung für die zweiten Ableitungen” —Institut für angewandte Mathematik der Universität, Bonn, 1978.Google Scholar
  11. [11]
    K.J. WITSCH: “The Geodetic Boundary Value Problem: a Uniqueness Result”—Institut für angewandte Mathematik der Universität, Bonn, 1978.Google Scholar

Copyright information

© Bureau Central de L’Association Internationale de Géodésie 1981

Authors and Affiliations

  • Fernando Sansò
    • 1
  1. 1.Istituto di Topografia, Fotogrammetria e GeofisicaPolitecnico di MilanoMilanoItaly

Personalised recommendations