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We establish a refined $L_p$-estimate ($p\geq 2$) for the stochastic heatequation on angular domains in $\mathbb{R}^2$ with mixed weights based on both,the distance to the boundary and the distance to the vertex. This way we cancapture both causes for singularities of the solution: the incompatibility ofnoise and boundary condition on the one hand and the influence of boundarysingularities (here, the vertex) on the other hand. Higher order $L_p$-Sobolevregularity with mixed weights is also established.

An $L_p$-theory for the stochastic heat equation on angular domains in $\mathbb{R}^2$ with mixed weights