A $W^1_2$-Theory of Stochastic Partial Differential Systems of Divergence Type on $C^1$ Domains

Abstract

In this paper we study the stochastic partial differential systems of divergence type with $\mathcal{C}^1$ space domains in $\mathbb{R}^d$. Existence and uniqueness results are obtained in terms of Sobolev spaces with weights so that we allow the derivatives of the solution to blow up near the boundary. The coefficients of the systems are only measurable and are allowed to blow up near the boundary.