  The Dirichlet problem for a Monge-Ampere equation corresponding to a
nonnegative, possible degenerate cohomology class on a Kaehler manifold with
boundary is studied. C^{1,\alpha} estimates away from a divisor are obtained,
by combining techniques of Blocki, Tsuji, Yau, and pluripotential theory. In
particular, C^{1,\alpha} geodesic rays in the space of Kaehler potentials are
constructed for each test configuration
