Improved estimates for the linear Molodensky problem

doi:10.1007/s00190-024-01846-1

Improved estimates for the linear Molodensky problem

2024-05-06

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DOI：10.1007/s00190-024-01846-1

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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 Sans & ograve; and Venuti (J Geod 82:909-916, 2008). Yet the result basically requires that S should have an inclination of less than 60 degrees \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$60<^>\circ $$\end{document} 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 degrees \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$75<^>\circ $$\end{document} . At the same time, the proof is made precise mathematically and hopefully more readable in the geodetic community.

Keyword:

Geodetic boundary value problem

Regularity of the telluroid

Spaces of harmonic functions

Improved estimates for the linear Molodensky problem

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