Inverse conductivity problems based on vector variational principles: the 2D case*

Abstract:  Electrical impedance tomography and Calder ́on’s problem is being intensely studied in the last decades. Both from the perspective of theory and of applications, it is a challenging and appealing problem. We focus on several direct vector, variational princi- ples to tackle the practical recovery problem of an unknown conductivity coefficient from boundary measurements. Despite difficulties associated with the vector nature of the prob- lems, including lack of (quasi, poly)-convexity, experiments show remarkable performance of some of the functionals examined.