Abstract:In recent years, many scholars have researched into the related problems of Dirichlet's weighted energy on circular rings. According to the recent results on Nitsche phenomenon of Dirichlet's weighted energy, a new weighted function is given to prove it. Combined with the new piecewise weighted function, by the use of the continuity of harmonic function, and the univalence of the minimum harmonic Dirichlet energy curve is examined, and the Nitsche condition of piecewise weighted function is obtained.