Abstract:

In this paper is  concerned with a ferromagnetic and antiferromagnetic functional in the case of p∈(n-1,n), n≥3. Applying the local analysis, the authors firstly deduced the regular estimate of this functional. Then the W^1,p_loc convergence of its regularized minimizer was proved. Based on these results and the established  corresponding estimate of the radial solution to the Euler system, the authors finally obtained the C^1,α  convergence and the estimate of the convergence rate of the radial minimizer.

Key words: ferromagnetic and antiferromagnetic functional, regularized minimizer, estimate of the convergence rate