SINGULARITIES OF ROTATIONALLY SYMMETRICAL SOLUTIONS OF BOUNDARY-VALUE-PROBLEMS FOR THE LAME EQUATIONS

We apply the theory of elliptic boundary value problems in non-smooth domains with conical points to rotationally symmetric solutions of boundary value problems for the Lame equations. The resulting expansion involves singular vector-functions which, in turn, depend on a parameter, alpha. We here present equations which determine the values of alpha for either stress-free or Dirichlet boundary conditions. We give a numerical algorithm whereby alpha can be computed and present some plots of the values obtained. The singular vector-functions are given explicitly and we present equations for the computation of the coefficients of the expansion.