GLOBAL MINIMIZER OF THE GROUND STATE FOR TWO PHASE CONDUCTORS IN LOW CONTRAST REGIME
GLOBAL MINIMIZER OF THE GROUND STATE FOR TWO PHASE CONDUCTORS IN LOW CONTRAST REGIME
复制标题
低对比度条件下两相导体基态的全局最小化
DOI：
--
复制
发表时间：
2014
期刊：
影响因子：
--
通讯作者：
A. Laurain
中科院分区：
文献类型：
--
作者：
A. Laurain
在二维和三维两种情况下，考虑了在球中分布两个给定体积比的导电材料以最小化具有Dirichlet条件的椭圆型算子的第一本征值的问题。假设两个电导率之间的间隙e很小(低对比度区域)。本文的主要结果是，利用关于e的渐近展开式和最优形状的小几何摄动，证明了在低对比度区域，第一本征值的全局最小值要么是中心球，要么是中心球和接触边界的中心环的并集，这取决于两种材料之间的预定体积比。
The problem of distributing two conducting materials with a prescribed volume ratio in a ball so as to minimize the first eigenvalue of an elliptic operator with Dirichlet conditions is considered in two and three dimensions. The gap e between the two conductivities is assumed to be small (low contrast regime). The main result of the paper is to show, using asymptotic expansions with respect to e and to small geometric perturbations of the optimal shape, that the global minimum of the first eigenvalue in low contrast regime is either a centered ball or the union of a centered ball and of a centered ring touching the boundary, depending on the prescribed volume ratio between the two materials.