# A global uniqueness theorem for an inverse boundary value problem

### Abstract

In this paper, we show that the single smooth coefficient of the elliptic operator $L_\gamma = \nabla \cdot \gamma\nabla$ can be determined from knowledge of its Dirichlet integrals for arbitrary boundary values on a fixed region $\Omega \subseteq \mathbf{R}^n$, $n\ge 3$. From a physical point of view, we show that an isotropic conductivity can be determined by steady state measurements at the boundary.

John Sylvester

Gunther Uhlmann