Convergence rates for Tikhonov regularization of coefficient identification in steady-state diffusion problems

A steady-state diffusion equation with mixed boundary values is investigated. If the conductivity $\alpha(x)$ is unknown, with the measured data $z^\delta=u(x)$ in $\Omega$, the $\alpha(x)$ can be uniquely determined. In addition, under a simple source condition, the convergence rates for the regularized solutions and approximate conductivity are achieved.