由平移法边界测量确定三维物体中两种材料体积分数的边界
Bounds on the volume fractions of two materials in a three dimensional body from boundary measurements by the translation method
摘要：
利用Tartar、Murat、Lurie和Cherkaev的平移方法，导出了三维导体中夹杂物所占体积的边界。他们假设已经对边界周围的三组电流通量和电压测量进行了电阻抗断层扫描测量。此外，假设包裹体和周围介质的电导率是已知的。如果边界数据（狄利克雷或诺依曼）是特殊的，即，这样的领域内的身体将是均匀的身体均匀，然后边界减少到那些米尔顿，从而当体积分数是小的Capdeboscq和Vogelius。
英文摘要：
Using the translation method of Tartar, Murat, Lurie, and Cherkaev bounds are derived on the volume occupied by an inclusion in a three-dimensional conducting body. They assume electrical impedance tomography measurements have been made for three sets of pairs of current flux and voltage measurements around the boundary. Additionally the conductivity of the inclusion and surrounding medium are assumed to be known. If the boundary data (Dirichlet or Neumann) is special, i.e. such that the fields inside the body would be uniform were the body homogeneous, then the bounds reduce to those of Milton and thus when the volume fraction is small to those of Capdeboscq and Vogelius.
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