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We study the second-order quasi-linear stochastic partial differentialequations (SPDEs) defined on $C^1$ domains. The coefficients are randomfunctions depending on $t,x$ and the unknown solutions. We prove the uniquenessand existence of solutions in appropriate Sobolev spaces, and in addition, weobtain $L_p$ and H\"older estimates of both the solution and its gradient.

A regularity theory for quasi-linear Stochastic Partial Differential Equations in weighted Sobolev spaces