Modified Dirichlet problem for a three-dimensional elliptic equation strongly degenerate on a line (Q1066353)

We consider in a three-dimensional domain of the Euclidean space the modified Dirichlet problem for the elliptic equation \[ (1)\quad Lu\equiv a(z)u_{zz}+(x^ 2+y^ 2)^{\alpha}(u_{xx}+u_{yy})+b(z)u_ z+c(z)u=0, \] which is strongly degenerate on a line, where the line of degeneracy intersects the domain considered.