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On a free boundary value problem of physical geodesy, II (existence)
Author(s) -
Witsch K. J.,
Leis R.
Publication year - 1986
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670080102
Subject(s) - mathematics , legendre transformation , argument (complex analysis) , boundary value problem , legendre polynomials , boundary (topology) , mathematical analysis , free boundary problem , value (mathematics) , topology (electrical circuits) , combinatorics , biochemistry , chemistry , statistics
The determination of the figure of the earth is considered as a local free boundary value problem of potential theory. In the C 1,ε ‐topology local existence is proved by means of Legendre transforms. This method also provides an elementary argument for the regularity of the solutions.