A Variational Principle for Solving the mixed boundary Value Problem and Calculating Directly the Potential Coefficients

A variational principle is presented in this paper for directly calculating the potential coefficients in solving the mixed boundary value problem. According to the principle, potential coefficients can be obtained directly in solving the mixed boundary value problems of first, second and third type. The principle can be used for studying Earth' s gravity field jointly applying the classical gravimetric(the gravimetric points are positioned using classical geodetic method such as trianglation and geometric levelling), satellite gravimetric (the gravimetric points are positioned by satellite positioning techniques) and satellite altimetric data.