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We consider the reconstruction of a diffusion coefficient in a quasilinearelliptic problem from a single measurement of overspecified Neumann andDirichlet data. The uniqueness for this parameter identification problem hasbeen established by Cannon and we therefore focus on the stable solution in thepresence of data noise. For this, we utilize a reformulation of the inverseproblem as a linear ill-posed operator equation with perturbed data andoperators. We are able to explicitly characterize the mapping properties of thecorresponding operators which allow us to apply regularization in Hilbertscales. We can then prove convergence and convergence rates of the regularizedreconstructions under very mild assumptions on the exact parameter. These are,in fact, already needed for the analysis of the forward problem and noadditional source conditions are required. Numerical tests are presented toillustrate the theoretical statements.

Numerical identification of a nonlinear diffusion law via regularization in Hilbert scales