  We consider the stochastic 2-dimensional Cahn-Hilliard equation which is
driven by the derivative in space of a space-time white noise. We use two
different approaches to study this equation. First we prove that there exists a
unique solution $Y$ to the shifted equation (see (1.4) below), then $X:=Y+{Z}$
is the unique solution to stochastic Cahn-Hilliard equaiton, where ${Z}$ is the
corresponding O-U process. Moreover, we use Dirichlet form approach in
\cite{Albeverio:1991hk} to construct the probabilistically weak solution the
the original equation (1.1) below. By clarifying the precise relation between
the solutions obtained by the Dirichlet forms aprroach and $X$, we can also get
the restricted Markov uniquness of the generator and the uniqueness of
martingale solutions to the equation (1.1).
