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We prove existence of martingale solutions for the stochastic Cahn-Hilliardequation with degenerate mobility and multiplicative Wiener noise. Thepotential is allowed to be of logarithmic or double-obstacle type. By extendingto the stochastic framework a regularization procedure introduced by C. M.Elliott and H. Garcke in the deterministic setting, we show that acompatibility condition between the degeneracy of the mobility and the blow-upof the potential allows to confine some approximate solutions in the physicallyrelevant domain. By using a suitable Lipschitz-continuity property of thenoise, uniform energy and magnitude estimates are proved. The passage to thelimit is then carried out by stochastic compactness arguments in a variationalframework. Applications to stochastic phase-field modelling are also discussed.

The stochastic Cahn-Hilliard equation with degenerate mobility and logarithmic potential