A uniqueness result for an inverse problem of the steady state convection-diffusion equation

Abstract

We consider the inverse boundary value problem for the steady state convection diffusion equation. We prove that a velocity field $V$, is uniquely determined by the Dirichlet-to-Neumann map, when $V\in C^{0,\gamma }(\Omega )$, $2/3<\gamma \le 1$, i.e. when $V$ is a Hölder continuous vector field with $2/3<\gamma \le 1$.

23 pages