最大化多相各向异性导体的第一特征值:凸化与均匀化

Maximizing the principal eigenvalues of multiphase anisotropic conductors: Convexification vs. homogenization

为使一类代表着几种各向异性材料混合物的椭圆型算子的第一特征值达到最大,本文考虑凸化问题和均匀化意义下的松弛问题.本文发现这两种问题的解在某种意义上是等同的,并建立了存在性结果和必要条件.

To maximize the principal eigenvalue of the elliptic operators for the mixture of several anisotropic materials, both convexification problems and relaxed problems by homogenization are considered. It is found that the solutions of the two types of problems are equivalent in some sense. Both existence results and necessary conditions are established.