The thesis treats the solution of the oblique boundary value problem of potential theory that plays an important role in physical geodesy, in particular in modeling the gravitational field of the Earth. Therefore, the boundary is the known surface of the Earth itself. The measurements can be considered as discrete scattered directional derivatives of the desired potential on the surface or even just on parts of that surface. The directions of these derivatives are usually given as the direction of the gravity gradient. They differ from the normal, because in general the Earth's surface is no equipotential surface of the gravitational potential.