  Higher-order estimates in weighted Sobolev spaces for solutions to a singular
elliptic equation for the stream function in an axially symmetric cylinder are
provided. These estimates are essential for investigating the existence of
axially symmetric solutions to incompressible Navier-Stokes equations in
axially symmetric cylinders. To derive the estimates the technique of
Kondratiev is incorporated. The weight has a form of a power function of the
distance to the axis of symmetry.
