On the completeness and uniqueness of the Papkovich-Neuber and the non-axisymmetric Boussinesq, Love, and Burgatti solutions in general cylindrical coordinates

Abstract

The exact conditions under which the Papkovich-Neuber, non-axisymmetric Boussinesq, non-axisymmetric Love and non-axisymmetric Burgatti solutions (to be defined below) are complete and unique for a general (not necessarily axi-symmetric) problem in general (not necessarily circular) cylindrical coordinates are investigated. They form four problems. The first one is the conjecture that any component of the curvilinear form of the Papkovich-Neuber solution can be omitted and also the general uniqueness of this solution in term of three harmonic functions. The remaining three concern the completeness and uniqueness of the non-axisymmetric Bousinesq, non-axisymmetric Love, non-axisymmetric Burgatti and a non-axisymmetric augmented Love solutions. Love's solution is shown to be incomplete for the case of a hollow sphere with the internal void pressurised.