Inverse boundary value problems. An overview

In this paper, we present an overview of some recent progress in inverse problems. We shall discuss several time independent problems. In general we consider a bounded region in ${\mathbb R}^n$, which represents a body, and a partial differential equation, or system of equations, which represents the physics inside the body. The problem is to deduce the interior physical parameters – coefficients of the differential equation – from measurements made at the boundary of the region. We begin with the simplest example.