Integral Equation Formulations for Geodetic Mixed Boundary Value Problems
نویسندگان
چکیده
We consider mixed boundary value problems in Physical Geodesy and study possibilities in order to transform them into a system of integral equations over the boundary of the domain. The system of integral equations can be solved numerically, by, e.g. boundary element methods, provided that (a) the mixed boundary value problem is uniquely solvable, (b) the system of integral equations is equivalent to the mixed boundary value problem, and (c) the matrix of integral operators is strongly elliptic. We introduce a method, first proposed by Stephan, which allows to derive integral equation formulations for all mixed boundary value problems relevant to geodetic applications. Moreover, the analysis of Stephan for the mixed DirichletNeumann problem may be generalized to the geodetic mixed boundary value problems, as well.
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