Improved estimates for the linear Molodensky problem

• Published in: Journal of geodesy Vol. 98; no. 5
• Main Authors: Sansò, Fernando, Betti, Barbara
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01-05-2024; Springer Nature B.V
• Subjects: Earth and Environmental Science; Earth Sciences; Geophysics/Geodesy; Harmonic functions; Mountain regions; Original Article; Geodetic boundary value problem; Regularity of the telluroid; Spaces of harmonic functions
• ISSN: 0949-7714; 1432-1394
• DOI: 10.1007/s00190-024-01846-1

The paper deals with the linearized Molodensky problem, when data are supposed to be square integrable on the telluroid
S
, proving that a solution exists, is unique and is stable in a space of harmonic functions with square integrable gradient on
S
. A similar theorem has already been proved by Sansò and Venuti (J Geod 82:909–916, 2008). Yet the result basically requires that
S
should have an inclination of less than
60
∘
with respect to the vertical, or better to the radial direction. This constraint could result in a severe regularization for the telluroid specially in mountainous areas. The paper revises the result in an effort to improve the above estimates, essentially showing that the inclination of
S
could go up to
75
∘
. At the same time, the proof is made precise mathematically and hopefully more readable in the geodetic community.