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We establish existence, uniqueness, and Sobolev and H\"older regularityresults for the stochastic partial differential equation $$du=\left(\sum_{i,j=1}^d a^{ij}u_{x^ix^j}+f^0+\sum_{i=1}^df^i_{x^i}\right)dt+\sum_{k=1}^{\infty}g^kdw^k_t, \quad t>0, \,x\in \mathcal{D}$$ given with non-zero initial data. Here $\{w^k_t: k=1,2,\cdots\}$ is a familyof independent Wiener processes defined on a probability space $(\Omega,\mathbb{P})$, $a^{ij}=a^{ij}(\omega,t)$ are merely measurable functions on$\Omega\times (0,\infty)$, and $\mathcal{D}$ is either a polygonal domain in$\mathbb{R}^2$ or an arbitrary dimensional conic domain of the type\begin{equation} \label{conic} \mathcal{D}(\mathcal{M}):=\left\{x\in\mathbb{R}^d :\,\frac{x}{|x|}\in \mathcal{M}\right\}, \quad \quad\mathcal{M}\in S^{d-1}, \quad (d\geq 2) \end{equation} where $\mathcal{M}$ isan open subset of $S^{d-1}$ with $C^2$ boundary. We measure the Sobolev andH\"older regularities of arbitrary order derivatives of the solution using asystem of mixed weights consisting of appropriate powers of the distance to thevertices and of the distance to the boundary. The ranges of admissible powersof the distance to the vertices and to the boundary are sharp.

Sobolev space theory and H\"older estimates for the stochastic partial differential equations on conic and polygonal domains