  We extend the main results obtained by Iwaniec and Onninen in Memoirs of the
AMS (2012). In the paper it is solved the minimization problem of $(\rho,n)$
energy of Sobolev homeomorphisms between two concentric annuli in the Euclidean
space $\mathbf{R}^n$. Here $\rho$ is a radial metric defined in the image
annulus. The key of the proofs comes from the solution to the Euler-Lagrange
equation for radial harmonic mapping. This is a new contribution on the topic
of famous Nitsche conjecture.
