A Sobolev space theory of SPDEs with constant coefficients in a half space

Equations of the form du = (a^{Script i signScript j sign}Script u sign_{cursive greek chiScript i signcursive greek chiScript j sign} + D_{Script i sign}Script f sign^{Script i sign}) Script d signScript t sign + Σ_{Script k sign}(σ^{Script i signScript k sign}Script u sign_{cursive greek chiScript i sign} + Script g sign^{Script k sign})Script d signScript w sign^{Script k sign}_{Script t sign} are considered for Script t sign > 0 and cursive greek chi ∈ ℝ^{Script d sign}₊. The unique solvability of these equations is proved in weighted Sobolev spaces with fractional positive or negative derivatives, summable to the power Script p sign ∈ (2, ∞).