On an inverse problem for anisotropic conductivity in the plane

Let $\hat Ω\subset \mathbb R^2$ be a bounded domain with smooth boundary and $\hat σ$ a smooth anisotropic conductivity on $\hat Ω$. Starting from the Dirichlet-to-Neumann operator $Λ_{\hat σ}$ on $\partial \hat Ω$, we give an explicit procedure to find a unique domain $Ω$, an isotropic conductivity $σ$ on $Ω$ and the boundary values of a quasiconformal diffeomorphism $F:\hat Ω\to Ω$ which transforms $\hat σ$ into $σ$.

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