Parameter estimation in an elliptic problem

Abstract: A new variational approach to solve the problem of estimating the (possibly discontinuous) coefficient functions $p$, $q$ and $f$ in elliptic equations of the form $-\nabla \cdot (p(x)\nabla u) + \lambda q(x) u = f$, $x \in \Omega \subset \mathbb{R}^n$, from a knowledge of the solutions $u_\lambda$.