Absolute Continuity of the Law of the Solution of a Parabolic SPDE

Let {u(t, x); t ≥ 0, 0 < x < 1} denote the solution of a white noise driven parabolic stochastic partial differential equation with Dirichlet boundary conditions. Using Malliavin′s calculus, we give a necessary and sufficient condition for the law of the r.v. u(t, x) to a possess a density.