论文标题
二维异质介质能力的渐近行为
Asymptotic behaviour of the capacity in two-dimensional heterogeneous media
论文作者
论文摘要
我们描述了相对于固定的开放式$ω$，平面中小集的不均匀两个容量的渐近行为。这个问题受两个小参数的控制：$ \ varepsilon $，包含的大小（不限制假定为球）和$δ$，即通过振动系数建模的不均匀性期间。我们表明，这种能力的行为为$ c | \ log \ e |^{ - 1} $。系数$ c $是根据振荡系数的最小值和相应同质矩阵的决定因素明确计算的，该矩阵的决定因素，其比例取决于$ | \logΔ|/| \ log log \ log \ log \ varepsilon | $的比例。
We describe the asymptotic behaviour of the minimal inhomogeneous two-capacity of small sets in the plane with respect to a fixed open set $Ω$. This problem is governed by two small parameters: $\varepsilon$, the size of the inclusion (which is not restrictive to assume to be a ball), and $δ$, the period of the inhomogeneity modelled by oscillating coefficients. We show that this capacity behaves as $C|\log\e|^{-1}$. The coefficient $C$ is explicitly computed from the minimum of the oscillating coefficient and the determinant of the corresponding homogenized matrix, through a harmonic mean with a proportion depending on the asymptotic behaviour of $|\logδ|/|\log\varepsilon|$.
