论文标题
传输问题的最佳估计值，包括具有不同符号的相对电导率
Optimal estimates for transmission problems including relative conductivities with different signs
论文作者
论文摘要
我们研究了在接近夹杂物的存在下，研究传输问题的梯度和高阶衍生物估计值。我们表明，在两个维度上，当圆形夹杂物的相对电导率具有不同的符号时，梯度和高阶导数独立于$ \ varepsilon $，即夹杂物之间的距离。我们还表明，对于一般平滑的严格凸起夹杂物，当一个包含是绝缘体而另一个包含是一个完美的导体时，任何订单的衍生物在任何维度上都独立于$ \ varepsilon $的限制。
We study the gradient and higher order derivative estimates for the transmission problem in the presence of closely located inclusions. We show that in two dimensions, when relative conductivities of circular inclusions have different signs, the gradient and higher order derivatives are bounded independent of $\varepsilon$, the distance between the inclusions. We also show that for general smooth strictly convex inclusions, when one inclusion is an insulator and the other one is a perfect conductor, the derivatives of any order is bounded independent of $\varepsilon$ in any dimensions $n \ge 2$.
