The insulated conductivity problem, effective gradient estimates and the maximum principle
The insulated conductivity problem, effective gradient estimates and the maximum principle
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DOI：
10.1007/s00208-021-02314-3
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发表时间：
2021-03
影响因子：
1.4
通讯作者：
B. Weinkove
中科院分区：
文献类型：
--
作者：
B. Weinkove
本文考虑两个单位球为绝缘夹杂的绝缘电导率问题，两个单位球之间的距离为一阶。溶液呈现电势。在维数上，在绝缘体之间的狭窄区域内，寻找电场梯度的最佳界限是一个开放的问题。Li-Yang最近证明了一些有序的界限。在本文中，我们使用一个直接的最大值原理参数锐化李杨估计。我们的方法给出了有效的下界，特别是接近1的无穷大。
We consider the insulated conductivity problem with two unit balls as insulating inclusions, a distance of orderapart. The solutionurepresents the electric potential. In dimensionsit is an open problem to find the optimal bound on the gradient ofu, the electric field, in the narrow region between the insulating bodies. Li-Yang recently proved a bound of orderfor some. In this paper we use a direct maximum principle argument to sharpen the Li-Yang estimate for. Our method gives effective lower bounds on, which in particular approach 1 asntends to infinity.