高维情形下铁磁与反铁磁泛函可正则化极小元的C^(1,α)收敛性

C^(1,α) Convergence of the Regularized Minimizer of Ferromagnetic and Anti-ferromagnetic Functional in Higher Dimensions

研究一类与铁磁和反铁磁相关的泛函模型,其中p∈(n-1,n),n≥3.利用局部分析技巧,讨论了这类泛函的正则性估计,证明了泛函可正则化极小元的W1l,o cp收敛性,并利用Euler方程解的正则性估计,得到此泛函径向极小元的C1,α收敛性及收敛速度的估计.

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.