Mathematics of reconstruction of the surface of discontinuity inside a body from observation data

我们考虑了从一致椭圆型方程无穷多解的区域边界上的柯西数据中提取关于有界域上的系数的几个信息的问题。为此，我们提出了三种数学方法。这些方法被称为探针法、封闭法和切片法。给出了它在无界区域上的柯西问题、逆散射问题和电导率逆问题中的应用。

We considered the problem of extracting several information about the coefficient in a uniformly elliptic equation in a bounded domain from the Cauchy data on the boundary of the domain of infinitely many solutions of the equation. We proposed three mathematical methods for the purpose. These are called the probe method, the enclosure method and the slice method. Applications to the Cauchy problem, the inverse scattering problem and the inverse conductivity problem in an unbounded domain are given.