Resumen
Considering the identification of a temperature dependent conductivity in a quasilinear elliptic heat equation from single boundary measurements, we proof uniqueness in dimensions $n \ge 2$. Taking noisy data into account, we apply Tikhonov regularization in order to overcome the instabilities. By using a problem-adapted adjoint, we give convergence rates under substantially weaker and more realistic conditions than required by the general theory. Our theory is supported by numerical tests.