void laplace_radial_2d_exact ( int n, double x[], double y[], double a, 
  double b, double u[], double ux[], double uy[], double uxx[], double uxy[], 
  double uyy[] );
void laplace_radial_3d_exact ( int n, double x[], double y[], double z[], 
  double a, double b, double u[], double ux[], double uy[], double uz[], 
  double uxx[], double uxy[], double uxz[], double uyy[], double uyz[], 
  double uzz[] );