Runge approximation and its application in Calderón type inverse problems

The classical Runge approximation property for uniformly elliptic equations states that it is possible to approximate solutions to an equation in the smaller domain by solutions of the same equation in the larger domain. In this talk, we will discuss how this property boils down to the unique continuation property, and how it leads to the Poisson embedding approach to the Calderón problem as one of its many applications in the inverse problems.