在这个课题中，我们将研究Calderon问题。Calderon问题的数学描述是内部的传导系数是否被边界的Dirichlet-to-Neumann 映射所决定. 即能否通过边界Dirichlet-to-Neumann 映射重构传导系数。另外，在一些实际问题中，通常只能得到部分边界的测量；那么内部的传导系数是否仍然被部分的边界Dirichlet-to-Neumann 映射所决定。具体来说， 我们将试图解决G. Uhlmann 的猜测，即Calderon问题的唯一性对Lipschitz的传导系数或更低正则性的传导系数成立。如果唯一性成立，我们将给出传导系数的重构。介于Calderon问题和边界刚性问题有很强的联系，我们也试图去解决关于边界刚性问题的R.Michel猜测。

In this project, we will study the Calderon problem. The mathematical description of the Calderon problem is whether or not the conductivity can be determined by the Dirichlet-to-Neumann map on the boundary. In other words, can we give the reconstruction of the conductivity from the Dirichlet-to-Neumann map on the boundary? On the other hand, in the practical application, we usually only get the partial boundary measurements. The natural question is whether or not the conductivity can be still determined by the Dirichlet-to-Neumann map on a portion of the boundary. More precisely, we will try to solve G. Uhlmann’s conjecture which is the uniqueness of the Calderon problem hods for Lipschitz conductivities or less regular conductivities. Furthermore, in view of the strong relation between the calderon problem and boundary rigidity problem, we will try to solve R. Michel's conjecture related to boundary rigidity problem.