On an inverse problem for anisotropic conductivity in the plane

Abstract

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

9 pages, no figure

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