In this paper, we consider the equations of stationary motion of electrorheological fluids in any dimension $n\ge 2$. We show that the first gradient of local solutions to the system has optimal $L^q$-regularity with some $q>1$ with respect to the one of the external force. This is achieved by comparison principle and a good $\lambda$-estimate.

中文翻译：

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电流变流体稳定流动的内部梯度估计

在本文中，我们考虑了任意尺寸的电流变流体的静运动方程 $ñ\ge 2$。我们表明，系统局部解的第一梯度具有最优的${\mathrm{大号}}^q$-有一些规律性 $q>\mathrm{1个}$关于外力之一。这是通过比较原理和良好的$\lambda$-估计。