PSEUDO-SOLUTION ON GEODETIC OVERDETERMINED BOUNDARY VALUE PROBLEMS

A higher step of study on the GOBVPs (geodetic overdetermined boundary value problems) is reached in this paper, which covers the proposal of new concept of pseudo-solutionon the GOBVPs, its strict definition of mathematics and solving principle. The so-called pseudosolution is a harmonical function having the property of optimum approximating the given boundary values in the sense of a relevant norm. Analytical expressions of the pseudo-solutions of two typical OBVPs for biboundary surfaces in physical geodesy, the problems S—D and S—N, are obtained, which is elegant and concise in form and convenient for practice, by using the derived formulas of norms of fractional exponential Sobolev's spaces in the case of spherical biboundary. The pseudo-solution is composed of two parts: the major is the solution of classical Stokes' problem, playing control role in field representation; the minor is correction term, serving the function of synergist and precision of the gravity field. Besides, a general case of the GOBVP is also dealt with.

A higher step of study on the GOBVPs (geodetic overdetermined boundary value problems) is reached in this paper, which covers the proposal of new concept of pseudo-solutionon the GOBVPs, its strict definition of mathematics and solving principle. The so-called pseudosolution is a harmonical function having the property of optimum approximating the given boundary values in the sense of a relevant norm. Analytical expressions of the pseudo-solutions of two typical OBVPs for biboundary surfaces in physical geodesy, the problems S—D and S—N, are obtained, which is elegant and concise in form and convenient for practice, by using the derived formulas of norms of fractional exponential Sobolev’s spaces in the case of spherical biboundary. The pseudo-solution is composed of two parts: the major is the solution of classical Stokes’ problem, playing control role in field representation; the minor is correction term, serving the function of synergist and precision of the gravity field. Besides, a general case