Solution of elliptic inverse problems using the Poincaré-Steklov operator

Abstract

We consider some inverse boundary problems which are to determine the coefficients or functions of elliptic differential equations inside the domain Ω from a knowledge of boundary conditions (the Cauchy data) on ∂Ω. An algorithm for the numerical solution of such problems is presented. The iterative methods and the theory of the Poincaré-Steklov operator are the basis of our consideration. This algorithm can be used for the solution of the inverse conductivity problem and for the determination of the potential in the Schrödinger equation.