论文标题
绝缘电导率问题的最佳梯度估计值超过两个尺寸
Optimal gradient estimates for the insulated conductivity problem with dimensions more than two
论文作者
论文摘要
在高对比度的复合材料中，电力（或应力）场可能会在夹杂物之间的狭窄区域爆炸。解决方案的梯度取决于$ε$，即包含物之间的距离，其中$ε$接近$ 0 $。通过使用最大原理技术，我们为任何任意形状的任何凸面包含$ n \ geq 3 $提供了dong-yan-yang估计值\ cite {dly}的另一个证明。该结果解决了\ cite {w}提出的问题，其中考虑了$ n \ geq 4 $的球形包含物。此外，我们还概括了上述结果，即接近接触点的平坦边界。
In high-contrast composite materials, the electric (or stress) field may blow up in the narrow region between inclusions. The gradient of solutions depend on $ε$, the distance between the inclusions, where $ε$ approaches to $0$. By using the maximum principle techniques, we give another proof of the Dong-Li-Yang estimates \cite{DLY} for any convex inclusions of arbitrary shape with $n\geq 3$. This result solves the problem raised by \cite{W}, where the spherical inclusions with $n\geq 4$ is considered. Moreover, we also generalize the above results with flatter boundaries near touching points.
