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Unique existence of analytically strong solutions to stochastic partialdifferential equations (SPDE) with drift given by the subdifferential of aquasi-convex function and with general multiplicative noise is proven. Theproof applies a genuinely new method of weighted Galerkin approximations basedon the "distance" defined by the quasi-convex function. Spatial regularizationof the initial condition analogous to the deterministic case is obtained. Theresults yield a unified framework which is applied to stochastic generalizedporous media equations, stochastic generalized reaction diffusion equations andstochastic generalized degenerated p-Laplace equations. In particular, higherregularity for solutions of such SPDE is obtained.

Strong Solutions for Stochastic Partial Differential Equations of Gradient Type