On the Linearization of the Geodetic Boundary Value Problem,
Abstract
The geodetic boundary value problem consists in determining an unknown closed surface from the boundary values of an external potential and its gradient. A rigorous mathematical formulation of this problem is given leading to a system of non-linear integro-differential equations. The formalism of differentiation in function spaces is applied yielding a linearized version which involves no further neglections and approximations. Tensor calculus is used in linearizing the various differential geometric quantities. The results are specialized to a linearization with respect to the equipotential sphere in which case the formulas of Stokes and Vening Meinesz are simultaneously obtained. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- May 01, 1971
- Accession Number
- AD0728632
Entities
People
- Peter Meissl
Organizations
- Ohio State University