  We compare the solutions of two Poisson problems in a spherical shell with
Robin boundary conditions, one with given data, and one where the data has been
cap symmetrized. When the Robin parameters are nonnegative, we show that the
solution to the symmetrized problem has larger (increasing) convex means. We
prove similar results on balls. We also prove a comparison principle on
generalized cylinders with mixed boundary conditions (Neumann and Robin).
