We study Green functions for the pressure of stationary Stokes systems in a (possibly unbounded) domain $\Omega\subset \mathbb{R}^d$, where $d\ge 2$. We construct the Green function when coefficients are merely measurable in one direction and have Dini mean oscillation in the other directions, and $\Omega$ is such that the divergence equation is solvable there. We also establish global pointwise bounds for the Green function and its derivatives when coefficients have Dini mean oscillation and $\Omega$ has a $C^{1,\rm{Dini}}$ boundary. Green functions for the flow velocity of Stokes systems are also considered.

中文翻译：

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斯托克斯系统压力的格林函数

我们在（可能是无界的）域 $\Omega\subset\mathbb{R}^d$ 中研究静止斯托克斯系统压力的格林函数，其中 $d\ge 2$。当系数仅在一个方向上可测量并且在其他方​​向上具有 Dini 均值振荡时，我们构造格林函数，并且 $\Omega$ 使得散度方程在那里是可解的。当系数具有 Dini 均值振荡且 $\Omega$ 具有 $C^{1,\rm{Dini}}$ 边界时，我们还为 Green 函数及其导数建立全局逐点边界。还考虑了斯托克斯系统流速的格林函数。