Extension of Boundary Control method to elliptic and parabolic problems, and its application to the Calderon problem

Abstract

We show that Boundary Control method, a method for hyperbolic inverse problems, is also capable of dealing directly with certain classes of elliptic and parabolic Inverse Boundary Value Problems; thus pointing towards Boundary Control method potentially constituting a means of unification of Inverse Boundary Value Problems. As an application we show that the Calderon problem can be dealt with directly via Boundary Control method, i.e. without reduction of the elliptic problem to a 'hyperbolized' problem.