An analysis of the linear fixed altimetry-gravimetry boundary-value problem

摘要

In this paper the linear fixed altimetry-gravimetry boundary-value problem is analyzed with respect to the existence and uniqueness of the solution. Nowadays, it is possible to determine very precisely points on the physical surface of the Earth by 3D satellite positioning and the problem is to determine the disturbing potential in an unbounded domain representing the exterior of the Earth. In order to establish realistic boundary conditions, a Dirichlet condition is imposed at seas and an oblique derivative condition on land. Then, mathematical methods are used within the frame of functional analysis for attacking the problem under consideration. Specifically, the Stampacchia theorem is used to decide upon the existence and uniqueness of the weak solution of the problem in a weighted Sobolev space. Finally, we confirm that the condition of validity for such a theorem has a geometrical interpretation.