The Cauchy problem for 1-dimensional nonlinear stochastic partial differential equations is studied. The uniqueness and existence of solutions in $cH^2_p(T)$-space are proved.

Existence and uniqueness theorems are presented for evolutional stochastic partial differential equations of second order in $L_p$-spaces with weights allowing derivatives of solutions to blow up near the boundary. It is allowed for the powers of summability with respect to…

We extend Krylov's $L_p$-solvability theory to the Cauchy problem for systems of parabolic stochastic partial differential equations. Some additional integrability and regularity properties are also presented.

A class of linear degenerate second-order parabolic equations is considered in arbitrary domains. It is shown that these equations are solvable using special weighted Sobolev spaces in essentially the same way as the non-degenerate equations in $R^d$ are solved using…