一类p-能量泛函径向极小元的C^(1,α)收敛性

C^(1,α) Convergence of a Radial Minimizer of p-Energy Functional

研究了具非S1值边界条件的p-能量泛函的径向极小元的收敛性.利用局部分析的技巧,推出了能量泛函的正则性估计,并由此得到泛函的径向极小元的零点分布在原点和单位圆周附近.在此基础上,利用Eul-er方程解的正则性估计,得到极小元的C1,α收敛性和收敛速度的估计.

The asymptotic behavior of the radial minimizer of a p-energy functional with non-S^1 Dirichlet boundary data is discussed. At first, by applying the local analysis, the authors deduce the regular estimate of the energy functional. Then, the zeros of the radial minimizer are located near the origin and the unit circle. Based on these results, the authors obtain the C^1,α convergence of the radial minimizer by establishing the corresponding estimate of the radial solution to the Euler system. Finally, the convergence rate is studied.