论文标题
部分可观测时空混沌系统的无模型预测
Gradient estimates for the insulated conductivity problem: the case of $m$-convex inclusions
论文作者
论文摘要
我们考虑了一个绝缘电导率模型，其中两个相邻的夹杂物为$ \ mathbb {r}^{d} $，当时$ \ mathbb {r}^{d} $当$ m \ geq2 $和$ d \ geq3 $时。我们在$β= [ - （D+M-3）+\ sqrt {（D+M-3）^{（d+m-3）^{2} +4（d-2）+4（d-2）+4（d-2）+4（d-d-2）+4（d-d-2）}+4（d-d-2）+4（d-d-2）+4（d-2）+4（d-d-}+4（d-2）+4（d-d-d-2）} $（MOS）（MOS）（Mor）（MOR）（D+M-3）^{2} +4（D-2）+4（d-d-2）}+4（d-D-2）} $（Mor）（MOR）（MOR）这两个绝缘子之间的$ \ varepsilon $趋于零。特别是，对于一类轴对称$ M $ -CONVEX夹杂物的爆炸率的最优性也证明了。
We consider an insulated conductivity model with two neighboring inclusions of $m$-convex shapes in $\mathbb{R}^{d}$ when $m\geq2$ and $d\geq3$. We establish the pointwise gradient estimates for the insulated conductivity problem and capture the gradient blow-up rate of order $\varepsilon^{-1/m+β}$ with $β=[-(d+m-3)+\sqrt{(d+m-3)^{2}+4(d-2)}]/(2m)\in(0,1/m)$, as the distance $\varepsilon$ between these two insulators tends to zero. In particular, the optimality of the blow-up rate is also demonstrated for a class of axisymmetric $m$-convex inclusions.
