Electrical Conductivity Reconstruction Using Nonlocal Boundary Conditions

In this paper we study existence, uniqueness and solution estimates to the mixed problem r ru = 0 with Dirichlet to Neumann map boundary conditions and Neumann boundary conditions. We then show how this can be used in the reconstruction of , given the relationship between u and its normal derivative on the boundary portion where we do not apply the Dirichlet to Neumann map. A numerical reconstruction scheme is also derived.