论文标题
绝缘电导率问题的梯度估计与一般$ M $ -CONVEX形状的夹杂物
Gradient estimates for the insulated conductivity problem with inclusions of the general $m$-convex shapes
论文作者
论文摘要
在本文中，在$ \ Mathbb {r}^{d} $带有$ d \ geq3 $的$ \ mathbb {r}^{d} $中考虑了带有两个接触或接近接近的夹杂物的绝缘电导率模型。我们在这两种情况下，在这两种情况下，在解决方案的梯度上建立了上限的上限，其中$ m \ geq2 $，这表明第一个非零eigenvalue在第一个非零eigenvalue在$ \ \ \ \ \ \ bb的eLliptic eigenvalue之间描述了两个夹杂物之间梯度的奇异行为。最后，还证明了两个接触轴对称绝缘子的估计值的清晰度，尤其是包括曲线立方体。
In this paper, the insulated conductivity model with two touching or close-to-touching inclusions is considered in $\mathbb{R}^{d}$ with $d\geq3$. We establish the pointwise upper bounds on the gradient of the solution for the generalized $m$-convex inclusions under these two cases with $m\geq2$, which show that the singular behavior of the gradient in the thin gap between two inclusions is described by the first non-zero eigenvalue of an elliptic operator of divergence form on $\mathbb{S}^{d-2}$. Finally, the sharpness of the estimates is also proved for two touching axisymmetric insulators, especially including curvilinear cubes.
