RT Journal Article
T1 Construction of the maximal solution of Backus' problem in geodesy and geomagnetism
A1 Díaz Díaz, Jesús Ildefonso
A1 Díaz Díaz, Gregorio
A1 Otero Juez, Jesús
AB The (simplified) Backus' Problem (BP) consists in finding a harmonic function u on the domain exterior to the three dimensional unit sphere S, such that u tends to zero at infinity and the norm of the gradient of u takes prescribed values g on S. Except for a change of sign, the solution is not unique in general. However, there is uniqueness of solutions in the class of functions with the additional property that the radial component of the gradient of u on S is nonpositive. This is the geodetically relevant case. If a solution u with this property exists, then u is the maximal solution of the problem (and -u the minimal one). In this paper we propose a method of successive approximations to get this particular solution of BP and prove the convergence for functions g close to a constant function.
PB Springer
SN 0039-3169
YR 2011
FD 2011-07
LK https://hdl.handle.net/20.500.14352/42412
UL https://hdl.handle.net/20.500.14352/42412
LA eng
NO DGISPI (Spain)
NO Research Groups MOMAT (Ref. 910480)
NO Geodesia (Ref. 910505)
NO Initial Training Network FIRST of the Seventh Framework Programme of the European Commission (Grant Agreement Number 238702
DS Docta Complutense
RD 24 abr 2025