p-Ginzburg-Landau型极小元的渐近性质与p-调和映射的关系

本文考虑的是一类p-Ginzburg-Landau型泛函极小元,当p∈(1,n)时的极限行为.研究了极小元的零点与p-调和映射的奇点间的关系,并证明了极小元在C1,γloc意义下收敛到p-调和映射.     

高维空间中一类Ginzburg-Landau型泛函的极小元的渐近分析

在空间H1,pg(Ω,Rn)中讨论如下一类变系数Ginzburg-Landau型泛函Eε(Ω)=∫Ωa(x)p|Δu|p+14εpb(x)(|u|2-β2(x))2dx的极小元列的渐近性质.这里2≤p0,m≤a(x),b(x),β(x)≤M,且a(x),b(x),β(x)是光滑函数.研究了当ε→0时极小元的渐近性态,证明了极小元列在H1,pg(Ω,Rn)中强收敛于某个元素,且得到了该元素所满足的微分方程边值问题.     

一类Ginzburg-Landau型泛函的径向极小元的渐近性

The behavior of radial minimizers for a Ginzburg-Landau type functional is considered. The weak convergence of minimizers in W1,n is improved to the strong convergence in W1,n. Some estimates of the rate of the convergence for the module of minimizers are presented.     

一类p-Ginzburg-Landau型方程解的整体收敛性

作者研究了一类p-Ginzburg-Landau型方程解的整体收敛性.通过建立正则化方程解的梯度的一致估计,最终证明了解在C^α意义下收敛.     

高维铁磁涟系统与p-调和映射

研究了与P-Laplace算子对映的铁磁链系统的Landau-Lifshitz方程，证明了该方程的从m（m≥3）维紧流形M（不带边界）映射到R3中的单位球面S2上的整体弱解的存在性；建立了p-调和映射理论与该方程的联系．     

到四元Grassmann流形的调和映射

利用奇异Darboux变换建立了四元Grassmann的因子分解并给出了其极小uniton数的上界估计。     

关于p-调和映射和正拼挤超曲面

本文主要讨论正拼挤超曲面的P－调和映射的不稳定性,从而推广了调和映射的相应结果．     

关于平面调和映射的Bloch常数的估计

考虑了拟正则调和映射和开的平面调和映射的Bloch常数, 得到了较好的结果,
所得结果推广了陈怀惠等及Grigoryan的结果.     

指数型调和映射

证明了在适当条件下,指数型能量和指数型调和映射是共形不变的.我们主要研究了指数型调和的黎曼淹没和等距浸入,还研究了与黎曼等距浸入相关的高斯映射是指数型调和.     

非齐次p-调和映射方程组弱驻点解的正则性

讨论非齐次p－调和映射方程组弱驻点解的内部正则性，证明了弱驻点解满足拟单调不等式，得到了弱驻点解梯度的Holder连续性。     

Uniqueness Theorem of the Regularizable Redial Ginzburg-Landau Type Minimizers

The author proves the uniqueness of the regularizable radial minimizers of a Ginzburg-Landau type functional in the case n - 1 < p < n,and the location of the zeros of the regularizable radial minimizers of this functional is discussed.     

p-Harmonic Maps and Convex Functions

p-harmonic maps (p ' 2) between Riemannian manifolds are investigated. Some theorems of Liouville type are given for such maps when target manifolds have convex functions.     

On the Zeros and Asymptotic Behavior of Minimizers to the Ginzburg-Landau Functional with Variable Coefficient

In this paper a partial answer to the fourth open problem of Bethuel-Brezis- Hélein [1] is given. When the boundary datum has topological degree ± 1, the asymptotic behavior of minimizers of the Ginzburg-Landau functional with variable coefficient \frac{1}{x_1} is given. The singular point is located.     

Global analysis of a p-Ginzburg-Landau energy with radial structure

This paper is concerned with the asymptotic behavior of a p-Ginzburg-Landau functional with radial structure as parameter goes to zero in the case of p≠2. By analyzing the functional globally, we show that the singularity of p-Ginzburg-Landau energy concentrates on the origin. By the fact the singularity can be balanced by some infinitesimal weight, we prove that an energy with a proper weight is globally bounded.     

Asymtotics of the Module of Minimizers to a Ginzburg-Landau Type Functional

The author proves that the module of minimizers for a Ginzburg-Landau type functional converges to 1. And the estimates on the convergent rate are also presented.     

含有杂质的Ginzburg-Landau泛函的径向极小元

研究了含有杂质的超导体的Ginzburg—Landau模型，给出了Ginzburg—Landau泛函的径向极小元的零点分布，并证明了径向极小元的惟一性。