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In this paper we prove the unique identifiability, module the naturalobstruction, for the Calder\'{o}n problem for quasilinear anisotropicconductivities in two dimensions from the associated Dirichlet-to-Neumann map.We reduce the problem to the isotropic case using isothermal coordinates. Forthis case, we prove the result by using the method of higher orderlinearization and Bukhgeim's CGO solutions.

Calder\'{o}n problem for quasilinear anisotropic conductivities in two dimensions