On stochastic partial differential equations with variable coefficients in C1 domains

Stochastic partial differential equations with variable coefficients are considered in C1 domains. Existence and uniqueness results are given in Sobolev spaces with weights allowing the derivatives of the solutions to blow up near the boundary. The number of derivatives of the solution can be negative and fractional, and the coefficients of the equations are allowed to substantially oscillate or blow up near the boundary.