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

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 $V \in C^{0,γ} (Ω)$, $2/3< γ\leq 1$, i.e. when $V$ is a Hölder continuous vector field with $2/3< γ\leq 1$.

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