  As an application of the theory of linear parabolic differential equations on
noncompact Riemannian manifolds, developed in earlier papers, we prove a
maximal regularity theorem for nonuniformly parabolic boundary value problems
in Euclidean spaces. The new feature of our result is the fact that, besides of
obtaining an optimal solution theory, we consider the `natural' case where the
degeneration occurs only in the normal direction.
