On a scalar fixed altimetry—gravimetry boundary value problem

For some years existence and uniqueness of the solution of a mixed altimetry — gravimetry boundary value problem is under investigation. Usually the size and the shape of the continental part of the Earth's surface is considered as unknown. This leads to a partly free and partly fixed mixed boundary value problem. A solution exists if the area of the continental part is sufficiently small. Obviously, this condition is not fulfilled in reality. Because the GPS is now fully operational, nowadays the size and the shape of the continental part of the Earth's surface can be considered as known, too. The aim of this article is to study the resulting fixed mixed boundary value problem and to prove the existence and uniqueness of its solution for an arbitrary distribution of land and sea at the Earth's surface.